My camera's shutter and mirror are sticky.

My camera has had a problem where if it is fired at a shutter speed slower than 1/125th, it has a pretty good chance for the shutter curtain to pop open only about a third of the way, almost completely close, and then the mirror gets stuck up. I can fix this by pushing the shutter all the way closed, and then the mirror will slap down and the camera will work fine. The batteries are fresh and working, the foam bumper for the mirror is the original one, but with absolutely no visible wear to it at all; it's not tacky in any way. Does anyone have any ideas?