I've been using white cement adhesive for kitchen and bathroom, and
they just fall off again. In fact when I cemented onto pva'd wood they
didnt stick at all, just lifted off when dry. Dont nkow what kind of
adhesive to choose, but obviously need something that works.

Ardicol D20 claims to stick to stable timber boards such as plywood.
Although intended for floor tiles, rather than wall, I'd be tempted to try
ArduFlex 7001 Timber System with Ardion 51 primer, although it doesn't claim
compatibility with walls...

Christian.