First step is to work out why it stops.
Easy way is to buy an inline red spark tester and fit it to the mower
Then get a can of carb cleaner.
Go mow
The instant it stops crank the engine and watch the spark tester for red flashes
No flashes = electrical problem
Red flashes but no fire = fuel / valve problem
whip off the air filter and give the carb a very short shot of cleaner and attempt to start
Engine fires = fuel supply problem
next try a shot of carb cleaner down a plug hole
Engine fires = valve problem.
and speaking of valves when was the last time you checked the valve lash ?
Let us know the results and we can take this furthe from there.
Your parts book & service manual are available from Cub on the web.
Download them both it will help greatly is we are all singing from the same song book.