To make things worse, because the mastic behind the remaining tiles has deteriorated, there's no guarantee that the fall-off won't continue. One is to remove all the remaining tiles, clean off the plywood, and relay them. Make sure your fixtures can accommodate the added width. Then reset the tiles using Thinset, a concrete powder mixed with water. Incidentally, tile professionals no longer use plywood or mastic.
Plywood can, over time, become damp enough to cause mold and mildew to develop behind the tiles.
Anyone who has experienced endless problems with discolored or mildewed grout can attest to this. Your third option is calling in a tile specialist and having him or her replace the whole thing, which is what we recommend. Your homeowners insurance policy will probably cover the cost, minus your deductible. It's shaped almost like a cheese slicer. You insert the filet into it and turn the handle, and it peels the skin off one side.