I actually studied this awhile back, but don't have my notes handy. I confess, I'm posting from memory:
Yes, it seems likely from Scripture that in the First Century church, Communion was celebrated every week. History shows that at least going back to the Fourth Century, it was celebrated weekly. This remained the case well into the Reformation.
Lutherans and Anglicans continued the very ancient practice of Communion as a part of every Sunday service. In fact, it STATES in the Lutheran Confessions that Lutherans celebrate Communion "every Sunday." But Calvinists and Zwinglians (who took a fairly low view of Communion) began to do so less often, sometimes as little as once a year.
In the USA, in spite of what the Lutheran Confessions clearly state, in the Nineteenth Century, many Lutherans began to delete it at times - it seems in reaction to anti-Catholicism ("seems to Catholic"). By the early Twentith Century, some American Lutherans were offering as little as 4 times a year (and then, not always on a Sunday). Some Lutherans in the USA were (oddly, absurdly) trying to not seem "Catholic" in a country where anti-Catholicism was strong. There has been a long (100 year!) process of returning to the nearly 2000 year practice of offering it every Sunday, indeed, still not all American Lutheran churches do so.
A blessed Lenten season to all....
- Josiah
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