Do you have to refrigerate leftover grilled corn-on-the-cob?
Yes, you should.  It does loose a little bit in reheating (we frequently use a microwave the second time around, if it's still on the cob), but it's fine for a few days in the fridge.

If you made excessive amounts, you might also consider removing it from the cob, bagging it, and freezing the kernels 'til you need them.  You can throw it into soups, salsa, pot pies, etc.

You can also freeze the stripped cobs to save for the next time you're making stock.