These members may associate an annual ceremony with a church that didn't understand Jesus' death as well as it should have. If we do it more often, then maybe we won't forget. There is truth on both sides of this issue. If it's done too often, it can lose its meaning. But it doesn't have to.
Many marriages have daily rituals that continue to be meaningful.
What is most important is not so much the frequency, but a clear understanding and explanation of the meaning. If the meaning is explained once a year and people remember it throughout the year, then once a year is enough. If the meaning is explained and the action is done several times a year with that meaning in mind, then several times is not too often. For some members, a more frequent communion will be helpful. Others may be more bothered by it than helped.