The lunar Sabbath is one of those teachings that sounds interesting and has some Scriptural evidences that can seem convincing. Everyone ought to study this for themselves of course…
Do your utmost to present yourself approved to Elohim, a worker who does not need to be ashamed, rightly handling the Word of Truth.” 2 Tim 2:15

The new moon is considered like a sabbath — a day of no work. Every month begins with a new moon. The first work day is the second day of the count followed by 5 more work days. That gets you through the 7th day of the month (new moon day plus 6 work days). The 8th day of the month is also the first weekly Sabbath of the month. Six more days of work gets you to the 15th as the next weekly Sabbath. Six more days of work and you come to the 3rd weekly Sabbath on the 22nd. Six more work days gets you to the 29th of the month, which is the last weekly Sabbath in the month. Then comes the next new moon, which is a not a work day but is a sabbath, but not a weekly Sabbath. Thus the weekly Sabbaths will always land on the 8th, 15th, 22nd, and 29th days of month, but dissension exists in the lunarian ranks because some lunar sabbatarians believe that the weekly Sabbath falls on the 7th, 14th, 21st and 28th days of the month.
Some months will end with the weekly Sabbath on the 29th followed by the new moon Sabbath the next day. More often, months will have an extra day or two between the last Sabbath and the next new moon day. Therefore you often have two or three Sabbaths or “non-work days” in a row before the new month begins.
The scheme also means that the Sabbath floats around and can land on any day of the week each month. If the new moon falls on a Tuesday, the Sabbath will be on succeeding Tuesdays of that month. Then it will flip to another day of the week the next month when the Sabbath is “re-set” by the appearance of the new moon.

the word week derives from a Hebrew word meaning “sevened” (sheb-u-wah). It is connected to a sequence of sevens, not to the new moon and not to more than seven. It begins with day one and ends with the seventh day, not the eighth day. Neither is “Sabbath” in any way linked etymologically to the word moon.
The lunar Sabbath when examined closely leaves your Sabbath cycle with days that are apparently “not counted in the six working days”! The Scriptures nowhere recognize them or address them and therefore can only be determined as an ADDITION to Scripture.

Proponents of the teaching claim that even a child can follow the lunar Sabbath, yet to the mind of a child the Scriptures are plain and simple when Yahweh says:
Six days you work, but on the seventh day you rest” (Exodus 34:21) 

The lunar Sabbath calculation flies in the face of not only history, but most importantly, Yahweh’s clear Commands. This is probably the biggest complaint against the lunar Sabbath in that it goes against Yahweh’s straight-forward Command to rest one day in seven. This Command is given in the Torah over and over and yet NOWHERE in Scripture do we find instruction that sometimes we might have to work eight days or rest for two days!
Just to emphasize this point, the following is the list of Scriptures that plainly (for children) instruct how the Sabbath works:

Genesis 2:1-3 “Thus the shamayim and the earth were completed, and all their array. 2 And on the seventh day Elohim completed His work which He had done, and He rested on the seventh day from all His work which He had made. 3 And Elohim barak the seventh day and qadosh it, because on it He rested from all His work which Elohim in creating had made.”
Take note of this Scripture, because it lays the foundation of the six working days followed by a rest (Sabbath) day. Scripture nowhere allows for or addresses multiple consecutive Sabbaths. No day can be added in and none can be ignored. All days must fit into the Fourth Commandment command of work for six and rest the seventh.

Exodus 20:8-11 “Remember the Shabbath day, to qadosh it9 “Six days you labour, and shall do all your work, 10 but the seventh day is a Shabbath of YHWH your Elohim. You do not do any work – you, nor your son, nor your daughter, nor your male servant, nor your female servant, nor your cattle, nor your stranger who is within your gates. 11 “For in six days YHWH made the shamayim and the earth, the sea, and all that is in them, and rested the seventh day. Therefore YHWH barak the Sabbath day and qadosh it.” 
Notice verse 11… Yahweh gave us HIS example in creation to rest one day in seven.

Exodus 23:12 “Six days you are to do your work, and on the seventh day you rest, in order that your ox and your donkey might rest, and the son of your female servant and the sojourner be refreshed.

Exodus 31:14-17 “‘And you shall guard the Shabbath, for it is qodesh to you. Everyone who profanes it shall certainly be put to death, for anyone who does work on it, that being shall be cut off from among his people. 15 ‘Six days work is done, and on the seventh is a Shabbath of restqodesh to YHWH. Everyone doing work on the Shabbath day shall certainly be put to death. 16 ‘And the children of Yisra’ĕl shall guard the Shabbath, to observe the Shabbath throughout their generations as an everlasting covenant17Between Me and the children of Yisra’ĕl it is a sign forever. For in six days YHWmade the shamayim and the earth, and on the seventh day He rested and was refreshed.’ ” 
Again the example of creation is used to define our seven day week.

Exodus 34:21 “Six days you work, but on the seventh day you rest – in ploughing time and in harvest you rest.”

Exodus 35:1 “And Mosheh assembled all the congregation of the children of Yisra’ĕl, and said to them, “These are the Words which YHWH has commanded you to do: 2 “Work is done for six days, but on the seventh day it shall be qodesh to you, a Shabbath of rest to YHWH. Anyone doing work on it is put to death.”

Leviticus 23:1-3 “And YHWH spoke to Mosheh, saying, 2 “Speak to the children of Yisra’ĕl, and say to them, ‘The Appointed Times of YHWH, which you are to proclaim as qodesh gatheringsMy Appointed Times, are these3 ‘Six days work is done, but the seventh day is a Shabbath of resta qodesh gathering. You do no work, it is a Shabbath to YHWH in all your dwellings.” 
NOTE: This text from Wayyiqra 23 is the defining chapter on the “Appointed Times” (moedim) of Yahweh… It initiates the list of these Qodesh (H-ly) Festivals by again repeating the six days of work followed by a Sabbath of rest. It really couldn’t be much clearer could it?

Deuteronomy 5:12 “Guard the Shabbath day, to set it apart, as YHWH your Elohim commanded you. 13Six days you labour, and shall do all your work, 14 but the seventh day is a Shabbath of YHWH your Elohim. You do not do any work.”

Yahweh also uses the ‘one rest in seven’ to examplify other ‘rests’ for His people and His land:
Exodus 21:2 “When you buy a Hebrew servant, he serves six years, and in the seventh he goes out free, for naught.” (also: Deut 15:12Jer 34:14)
Exodus 23:10-11 “And for six years you are to sow your land, and shall gather its increase, 11 but the seventh year you are to let it rest, and shall leave it…” (also:  Lev 25:3)

Consider how the manna was regularly provided each week. When Israel was in the wilderness Exodus plainly teaches that the manna fell for six days, with a double portion falling on the sixth day because none would fall on the seventh-day Sabbath. This went on continuously for 40 years:
Exodus 16:4-5 And YHWH said to Mosheh, “See, I am raining bread from the shamayim for you. And the people shall go out and gather a day’s portion every day, in order to try them, whether they walk in My Torah or not5 “And it shall be on the sixth day that they shall prepare what they bring in, and it shall be twice as much as they gather daily.”
Notice how Yahweh puts forward a “test” to see if we “walk  in His Torah or not.” They were to gather enough for TWO days on the sixth day of a week, and continues…
Exodus 16:25-26 And Mosheh said, “Eat it today, for today is a Shabbath to YHWH, today you do not find it in the field. 26 “Gather it six days, but on the seventh day, which is the Shabbath, there is none.” 

Nothing is said about a big interruption of this weekly manna cycle every fourth week by a couple of additional days at the end of the month when the new moon resets the week. If there were two or three rest days as the lunar Sabbath teaching requires, then there would be some mighty hungry Yisra’elites!

To mention such a critically important lunar interruption in the 7-day week could not possibly have slipped Yahweh’s mind. It is inconceivable that He would not have warned Israel to prepare for it! After all, He warned them to be sure to gather extra on the sixth day to make up for none on the weekly Sabbath. So why did He not tell them also to gather extra manna the sixth day to eat on the seventh, eighth and possibly ninth day at month’s end? Obviously no lunar-added days ever existed.

The count to the Feast of Weeks or Pentecost also reveals the error in the lunar sabbath teaching. Not only must there always be exactly seven days every week in every month of Yahweh’s calendar (by Fourth Commandment authority), but the count to Pentecost must also be seven complete weeks of seven days each, all adding up to exactly 49 days. 
“And from the morrow after the Shabbath, from the day that you brought the sheaf of the wave offering, you shall count for yourselves: seven completed Shabbathoth. ” Leviticus 23:15
Pentecost means 50th. It takes exactly 50 days to arrive at Pentecost – seven Sabbaths of precisely seven days each or 7 x 7 + 1 = 50. Partial weeks or extra days don’t compute. 
Scripture calls the this Festival of ‘Weeks’ which is the Hebrew ‘shabua’ and literally means “sevened” not “lunared.” After your seven sevens are over and complete, then you observe the Feast of Weeks (Pentecost.) You cannot get 7 Sabbaths to equal 49 days under the lunar sabbath scheme. This fact alone proves the lunar scheme bogus.

It seems all too clear that our Sabbath day (not days) of rest simply comes after working for six days. The lunar Sabbath simply relies on too much number juggling in Scripture to be valid and goes directly against all the Scriptures quoted above. This does not mean that the cycles of the moon do not dictate when a new month begins or ends. (see study below) 
By all means, examine this teaching for yourself, (prove them all. Hold fast what is good.” 1Th 5:21 ) but you too may find it difficult to discount all the Scriptures defining a 7 day week.