Why does communion frequency vary in different denominations? Different churches celebrate the Eucharist (Communion, Lord's Supper, ...) with different frequency. At one extreme, Catholic and high Anglican churches tend to celebrate it at least daily. Many Protestant churches offer it only once a month, though they will have a Sunday service each week. Some churches have Communion even less often - quarterly or annually.

What factors have caused the divergence in practice (between Catholics and Protestants) and how does each modern model compare to the frequency of its celebration in the early Church?
As you note, there are lots of different traditions here. My ancestry is Scottish and some old Scottish churches only celebrate communion once a year. I've looked through the some liturgies for these services that basically run all day, and it's quite an affair. I have even heard it advocated that once in a life-time ought to do the job, sort of like baptism. I don't think this is at all the spirit of the thing we find in the NT.

On the other end of the spectrum are those who say that every meal we eat together as believers counts, so basically we do it a couple times a day. For several reasons I don't think this argument holds much water.

By personal background growing up was the "traditional" once a month celebrations. I wouldn't argue that this practice is inherently wrong or sinful, but I think it is arbitrary and not the best representation of what the Lord's Supper is supposed to be about.

I believe the best representation and celebration of the Lords Supper is to do it once a week during the normal Sunday gatherings. This is consistent with the description we have of the early church gathering together (we know they did this specifically in celebration of the resurrection on the first day of each week) and the description we have of them celebrating the sacrament whenever they were gathered together.