Dave -
My guess (and it is only that) is that the bead of caulk is what keeps the sink from moving as the TM vibrates on down the road - and the movement is what is loosening the clips. Tell me, when you first pulled it out, was it bedded in caulk (it should have been)? If so, then you know that caulk can be removed.
If you are really dead set against caulking, how about fabricating a big "gasket", I guess you'd call it, out of some sort of non-slip rubber sheet stock. You know, the stuff they make jar openers out of? You might get a bigger chunk out of a silicone cookie sheet from the kitchen store.
Just a thought. Waterproof, easy to cut, not expensive, grippy ...
Bill
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