I have a 1 year old Cub Cadet lawn tractor that will start and stay running if I start it by priming the carburetor with a little gas. Fuel filter and fuel pump seem to be working. When I stop the tractor, basically it automatically turns the engine off when I get off the seat, it will not restart. The only way to get it running again is to do the same - put a little gas in the carburetor. What else should I check?

What make, model and HP engine???
 
Has it been sitting / not run for an extended period of time?
 
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It’s a 24HP V-Twin Kohler engine and yes it’s been sitting in storage all winter. I think it may be a temporary issue so I’m going to keep running it this week and see if the problem resolves itself with more usage.

Un-less you drained the carb before storage, the carb (likely main jet) is clogged with varnish / crap.
 
Pull the carb and the bowl to access the jets and remove varnish and plugged jets.
 
As your going to run the machine currently, put in a very strong dose of Seafoam or 
Yamaha Ring Free..  
 
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I will certainly give this a try..thank you!