Dave,
What do you mean "snaps on"? The muffler is threaded and you should be screwing the muffler on to the short pipe that comes out of the had of the engine. Also, on each end of that short pipe should be a lock nut. This is simply a nut that you should screw all the way onto the pipe. Then screw the pipe into the engine and get it in the position you want it, and back the lock nut out to where it contacts the head of the engine and tighten it down. The same on the muffler end of this pipe. Screw the muffler onto the pipe and then back the lock nut down to the muffler, and tighten it down. These lock nuts will keep the muffler and the short pipe from vibrating loose while the engine is running.

From what you say about the muffler "snapping on" it sounds like the threads inside of the muffler have been stripped out. If this is the case then you will have to replace the muffler.

Ken