It sounds like a gap in the plumber's putty or caulk, or none at all, between the rim of the sink and the counter top. I'd recommend removing the sink and doing a proper installation.
If any partical board is used in the construction of the counter or cabinet, it will swell when it absorbs water and is not repairable.

take a look at the photos 2. and 3. below halfway on page. woman in purple-blue shirt/blouse dropping stainless sink into black 'formica' counter: http://knol.google.com/k/kitchen-faucet-installation
i like to seal (just one coat wall primer or whatever primer) the cut edge and underside of the particle board.
also, don't use putty. use the "35 year" (or whatever higher number of years) siliconized latex. don't need caulk with mildew additive, because exposed gap under sink rim edge is super narrow (and counter is food prep surface).
you might check if the clips in photo 3. are tight and are pressing against firm particle board (not become fluffy)
i like to use more clips. 3 on each side, 4 front and 4 rear. ss sink rims are not always straight (maybe because I've reinstalled the used sinks more often than installing new ones ;-) )

if you creatively brace behind the parts going saggy, you can keep it going for years. it takes time, and edges of epoxy or caulk may show. I've fixed soaked shower tile on sheetrock (big no-no from the 1970s) One has lasted for more than a decade. the other i heard was renovated (modernized), but was probably still good.
1960's formica counter with separate splash was gapping. I epoxied "1/4 round" aluminum to close the joint.
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image robbing :-)
http://www.highlandsdesigns.com/images/vanity_inside_front_combo_500w.jpg
inside view of fake drawer fronts.