As with all other subjects, if men and the Bible have parted ways with reference to the answer of this question (and many have) then it is imperative that the Bible teaching be accepted, and the human practice rejected.  The Bible teaches very plainly about the Lord’s Supper in various passages, we shall only deal with a couple of those.
    The Bible teaches in Acts 20:7 that the disciples would come together on the first day of the week to break bread.  This is the equivalent of our Sunday.  It should also be implied that there was nothing special in this passage about their observing the Lord’s Supper on that day (as was their habit).  What made this particular first day special was that Paul was preaching.  This is evidence of a common practice then among the early church:  observing the Lord’s Supper on every week’s first day, i.e., each Sunday.
    While I Corinthians 11:23-28 does not teach that the Lord’s Supper must be observed on the first day of the week it does teach that a remembrance must be made, and the original language indicates a continuance, or regularity, of the practice.  In fact verse 25 reads “as oft as ye drink it.”  The Lord’s Supper is not just a one-time thing.  It is an observance that must be made perpetually.
    With these two passages in mind let it be understood that observing the Lord’s Supper is a necessity.  Let it also be observed that observing the Lord’s Supper is not a one-time action.  Further the Lord’s Supper is to be observed weekly, specifically on the first day of the week (per approved apostolic example):  Sunday.