To be sure, there is evidence for such regularity in the New Testament. In Acts 2:42, Luke describes how the earliest Christians "continued steadfastly in the apostles teaching, the fellowship, the breaking of bread and the prayers." The breaking of bread (communion) was as regular as the teaching, the fellowship and the prayers. Some 25 years later, after the church had expanded throughout the Mediterranean area, Luke tells how Paul came to Troas and waited several days until, as he says, "on the first day of the week, when we were gathered to break bread, Paul began talking to them ... " It appears that it was the custom to meet on the first day for the observance of the Lord's Supper.
It seems appropriate that we too should gather on the first day to "break bread". It is a good tradition. This answer satisfied me for a long time (I don't always catch on quickly),until one day it occurred to me that doing something simply because others have done it, even done it over a long period of time, is not enough. Tradition is valuable and helpful, but is it enough reason to continue doing something? Isn't there a more fundamental question that must be asked? What is behind this tradition? What is the fundamental reason for observing the Lord's Supper that drove the earliest Christians, and the church ever since then, to meet regularly for the observance?
Many texts in the New Testament, with many answers, could be given but if I had to point to just one it would be the reason given in 1 Corinthians 10:16-17, which seems to be saying that the Lord's Supper connects us to both Christ and the church in essential ways. Here is how Paul says it: "Is not the cup of blessing which we bless a sharing in the blood of Christ? Is not the bread which we break a sharing in the body of Christ? Since there is one bread, we who are many are one body; for we all partake of the one bread."
The blood of Christ ... the one body ... symbolized in these elements ... in this communion we are connected to the blood that forgives and the body that unites. What greater reason could we have to maintain the tradition and to "continue steadfastly in the apostles teaching, the fellowship, the breaking of bread and the prayers"?