I have proposed to our church that we move our communion service to a more regular observance. It isn't so much that there is resistance to the idea as it is apathy to the idea.
Come to think of it, it is interesting that a charge easily made against churches concerning their practice of the Lord's Supper would be that it is more of an add on to the regular service, more like a funeral than a celebration, and overall, "an ordinance of apathy." So it should probably not be a suprise that changing it ("change" being a bad enough thing in its own right for some) would produce apathy.
The primary argument I have heard against moving to weekly Communion has been that it would become "too repetitious" and that people would take it for granted. I don't see how having it monthly has eliminated this as a problem. I would actually argue that if this has become a problem in your church, you should do it more and not less.
But my family and I had the privilege of hearing pastor Josh Gelatt of Indian River Baptist Church, speak to his church about the various reasons to celebrate communion more, not less and to make it the focus of the service rather than the add on. Thank you pastor for your encouragement. Some folks who attended with me wanted to know if pastor Josh was stealing my notes. He has on numerous occassions repeated the same thing to his church that I propose to mine. (I'd like to think that we both get it from studying the Bible...)
So I am going to finish what I believe God is leading us to do as a church and see it through. There may be resistance, but if Communion becomes too repetitious or an 'add on' to worship, the problem is never with the ordinance that the Lord told us to do 'often,' but with US.