If you had a decompressor problem I'd expect difficulty starting the engine rather than difficulty keeping it going. If you want to eliminate the decompressor as a possibility you can just unscrew it and screw an ordinary spark plug into the hole so you can start and run the engine on full compression. That will also let you feel the strength of the compression.
Have you checked the intake pipe for leaks? Are you sure the carburetor float bowl is not flooding? Have you started it without the air cleaner? (It can chug and stop as easily from rich mixture as from lean).
