I have the same problem on my 04 SS, but it looks like everything under the seat is in order: no broken connections or anything... I'm going to talk to the dealership about it tomorrow, I'll let you know if I find anything interesting.
the heater grids are known to go bad. They used to have a kit to fix it, but the last time I replaced them, was a while ago, now you have to get the whole seat cover on some vehicle. Check with your local dealer to see if you need the grids or the seat covers.