The expression "the Lord's Supper" is found only once in the New Testament. It appears in 1 Corinthians 11:20, where Paul was discussing the observance of the New Testament Passover. Jesus Christ Himself specifically referred to this observance as the Passover (Luke 22:8, Luke 22:11, Luke 22:15). He observed it, with the new symbols of bread and wine, on the date specified in Leviticus 23. This annual observance should be kept on the 14th day of the first month on the Hebrew calendar.
The Passover is observed as a memorial to Christ's death (1 Corinthians 5:7; 1 Corinthians 11:20-27). It takes place just once a year. This is certainly the custom of memorial observances described in the Bible, and it is the typical pattern of secular memorial observances.
As a youth, Jesus observed the Passover annually with His family at the specified time (Luke 2:41). He continued this yearly practice with His disciples (Luke 22:7-15). After His death and resurrection, the early Church continued to observe the annual festivals listed in Leviticus 23. For example, Luke records that Jesus' followers met to observe the Feast of Pentecost: "When the Day of Pentecost had fully come, they were all with one accord in one place" (Acts 2:1).
Scripture gives no hint of the early Church adding to or changing the dates God appointed for observing His festivals. The phrase in 1 Corinthians 11:26—"for as often as you eat this bread and drink this cup"—does not mean at any time members might arbitrarily choose to partake of these symbols. It means whenever they actually did partake of them as part of the Passover ceremony—which was once a year. Paul was simply pointing out that by observing the New Testament Passover each year on the appropriate day, members were "proclaim[ing] the Lord's death till He comes."
The Bible specifies that the Passover ceremony should be observed annually. As a memorial of Jesus' death, it should be observed once a year at the specified time rather than whenever one chooses.
Following the original disciples' example, we should observe the Passover at the beginning of the evening of the 14th day of the first month of the Hebrew calendar. (The corresponding contemporary calendar dates are available in the Bible Study guide God's Holy Day Plan: The Promise of Hope for All Mankind.)