Q.If the early church "broke bread" whenever they came together, why do we celebrate just once a month?
High Church Denominations
Many churches do celebrate communion during every service such as the Roman Catholics or "high church" Protestant denominations who practice liturgical service.
But, the Bible doesn't tell us how often we are supposed to observe the Lord's Supper, although you are a good student to see that the early church participated frequently - if not every time they met. Acts 2:42 says:
…"they devoted themselves to the apostles' teaching and fellowship, to the breaking of bread and the prayers" (ESV).
The Lord's Supper took the place of the Old Testament Passover. The Passover commemorates the deliverance of the children of Israel out from a life of slavery in Egypt. Because Passover was celebrated just once a year, many churches serve communion only once yearly, too - usually at Easter.
Weekly, Monthly, Quarterly
Other churches observe it every week. Some serve it once a month, and others once every three months. As you can see the frequency of communion depends upon the traditions of your particular church and denomination.