The Gospel accounts make clear that this was the Passover (Luke 22:8, Luke 22:11, Luke 22:15)—with Jesus revealing new significance to the occasion, the partaking of the bread and wine signifying the acceptance of His sacrificial death. In fact, Paul earlier in 1 Corinthians 5:7 says that "Christ, our Passover, was sacrificed for us."
Passover was an annual occasion, coming on the 14th day of the first month on the Hebrew calendar (Leviticus 23:5). As a youth, Jesus Himself observed the Passover annually with His family at the specified time: "Now his parents went to Jerusalem every year at the feast of the Passover" (Luke 2:41). He continued this yearly practice with His disciples, as is evidenced by the four Passovers of His ministry recorded in the Gospel accounts, ending with the last one, the night before He was killed.
After Christ's 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 (Acts 2:1).
The Passover was likewise still observed, but now as a memorial to Christ's death—He being the true Passover Lamb. Even in secular society, it is customary to observe memorials on an annual basis. Moreover, this being the Passover, it was already an annual occasion observed on the same day each year on the Hebrew calendar.
There is nothing to indicate that Christians might arbitrarily choose to partake of the bread and wine representing Christ's sacrifice at some time other than the time decreed in the Bible—the time of Passover at the beginning (that is, in the evening) of the 14th day of the first month on the Hebrew calendar.
When Paul said "as often as" you partake of the bread and wine symbolically, he did not mean as often as you choose to of yourself, as many think. He simply meant whenever or every time Christ's followers actually did partake of them as part of the Passover ceremony—which was once a year on the night Christ was betrayed. The New Living Translation says, "... every time you eat this bread and drink this cup" (emphasis added).
In summary, notice this paragraph from our Holy Day booklet: "The Bible specifies the yearly observance of the Passover, and history records its annual celebration as the practice of the early Church. Passover, as a memorial of Christ's death, is to be observed annually rather than whenever or however one chooses, just as all the other annual festivals are to be kept once a year. Neither Jesus Christ nor His apostles indicated that we should change when or how often we observe any of God's festivals".
This free Bible study aid booklet, God's Holy Day Plan: The Promise of Hope for All Mankind, also contains the equivalent modern calendar dates for the annual festivals.