On the one hand, I agree with everyone who says to replace it; a 14 year old
WH is too old to screw with. On the other hand, a WH cannot leak
intermittently, which is why the warranty guy is confused. It either has a
hole, or it doesn't.

All I can think is that your t&p valve is not functional and occasionally
the pressure gets way too high and forces a leak that doesn't occure at
normal pressure. (I had an improperly soldered valve at 92psi that is just
fine after after i put a pressure reducer on. Same idea.) Do you test the
valve periodically as required? If not, it could be crudded shut.