Is it likely that first century Christians did not hold this ritual only once a year, but did so frequently?
It is certain that the Eucharist was the weekly activity of the early Christians. That is, their weekly sservices looked very much like Catholic, Orthodox, Anglican, or Methodist services and nothing whatever like the JW meeting. Consult St. Justin Martyr's First Apology, dating from around 135 AD, which attempts to explain the new Christian religion to the Romans, especially chapters 65-67. In 67, Justin offers an explanation of the weekly Christian service, which will be familiar to anyone from a liturgical tradition:
And on the day called Sunday, all who live in cities or in the country gather together to one place, and the memoirs of the apostles or the writings of the prophets are read, as long as time permits; then, when the reader has ceased, the president verbally instructs, and exhorts to the imitation of these good things. Then we all rise together and pray, and, as we before said, when our prayer is ended, bread and wine and water are brought, and the president in like manner offers prayers and thanksgivings, according to his ability, and the people assent, saying Amen; and there is a distribution to each, and a participation of that over which thanks have been given, and to those who are absent a portion is sent by the deacons. And they who are well to do, and willing, give what each thinks fit; and what is collected is deposited with the president, who succours the orphans and widows and those who, through sickness or any other cause, are in want, and those who are in bonds and the strangers sojourning among us, and in a word takes care of all who are in need. But Sunday is the day on which we all hold our common assembly, because it is the first day on which God, having wrought a change in the darkness and matter, made the world; and Jesus Christ our Saviour on the same day rose from the dead. For He was crucified on the day before that of Saturn (Saturday); and on the day after that of Saturn, which is the day of the Sun, having appeared to His apostles and disciples, He taught them these things, which we have submitted to you also for your consideration.
So, there you have it.
There is some irony in the observation that the JWs have gone to substantial lengths lately to make it seem, by way of illustrations, that the early Christians did things like go door-to-door. They did not, of course, and neither did their worship services look remotely like the JW's song, sermon, and study meetings. The JW conceit that they are re-discovering the authentic practices of early Christianity is as false as their conceit that they are re-discovering the authentic doctrines of early Christianity.