New cameras, same minor, nagging problem...

It's possible.  I had that problem once with my older Olympus C2100 UZ (which I still have and it still works).  I haven't had it since with any of my Olympus cameras.  The only thing that has changed signficantly is how I clean and store them. They are never put away after use without being cleaned first with a damp cloth.
FWIW, for sticking the rubber back, I've had good experience with Devcon rubber adhesive. The rubber and the area it's going to be stuck to do need to be cleaned properly first.

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Brian Steele
http://mypages.spiceisle.com/brian