I didn't see anyone mention that there possibly is a safety switch on the seat. They are generally normally closed so the engine won't run until pressure on the seat opens it.Out of curiosity you might try pushing (maybe holding) the button and then try engaging the pto and see if it stays running. As for testing or bypassing that varies from one model to the next. We avoid discussing specifics on bypassing safety switches here for legal reasons. But it's a pretty basic circuit normally with switches that are either normally open or closed (short) actuated by the linkage to the reverse pedal or when the shift lever is placed in the reverse gear (depending on the type of transmission you have.)
Normally a safety switch issue will cause the engine to shutdown with no sputtering. I suppose you could have a bare wire partly shorted to the frame or a partly shorted or open switch. But if the carb is out of adjustment, especially on the lean side that could also cause a stall under load. Does it throttle up from an idle smoothly without hesitation? If you load the engine say by pulling a heavy cart uphill can you hear the governor kick in without hesitation to maintain the engine speed under the load?
Another thought might be to check that your mower deck (assuming that is what your pto is currently driving) does not have a seized up bearing or something jamming up the blades or belts such as a tree limb in the belt path or caught between the belt and one of the pulleys.
