If the claw servo is the only one that repeatedly fails, and they are all the same type and on the same 6V supply, it cant be the PSU. However, check the ground to the claw servo, I bet it doesn't like having +6V applied with the control signal low and a missing ground.
Otherwise, IMHO the most likely explanation is its overloaded, probably because its commanded resting position is outside of the mechanical limits imposed by the claw mechanism travel. Edit: Andy shares my opinion and posted while I was replying.