Yes this happens. These gaskets are made of rubber and are in a place where they are constantly subjected to hot water. After only a couple of years, the gasket inside the pressure and temperature relief valve hardens. Since it is in the off position, its not a problem, but if you open it, now you have a problem. Since the gasket is hard, it does not want to reseat. You can try a lot of temp fixes, but I have found replacing it the easiest solution. Since they are only about 8 bucks, all you have to do is shut off the water to the water heater, drain it down just below the level of the P&T, then remove the old one. Make sure you buy a 3/4 P&T a 100 xl is the model you want. You can pretty much pick it up at any hardware store. Then remove the old one, with a pipe wrench, make sure you remove the drop tube first. Then dope up the new one with teflon tape first, then a little teflon pipe dope on the threads of the P&T only. The pipe dope helps prevent the teflon tape from slipping when you turn it into the female threads. Reinstall it into the water heater tight enough to prevent it from leaking, but not so tight you break off the brass threads. Typically you should have about 3 to 4 threads left on the P&T outside the water heater.
Turn on the water and check for leaks slowly. If it doesn't leak, relight the water heater and enjoy your sucess.