Either the output pressure is too high (it's set too high or the seat is damaged and it's creeping) or one of the piston o-rings needs replacing.
The piston can be accessed without empty the tank or fully dismatling the reg. Unscrew the adjuster cap, remove the shim and spring, and carefully pull the piston out with a pair of fine-nosed pliers (If it's not coming out without risking damage, then you will have to empty the tank and take the reg apart to push the piston out from the inside.)
Check the 3 o-rings on the piston - two around the outside, and one small one in the end. Replace if at all damaged; grease them anyway and put it back together.