Tractor dies.

[Herkfixer]

Kubota 7310 works fine while operating and then the engine quits. I have discovered that if I move the forward / reverse pedal when it starts to die, I can prevent it from dying.
Another instance is when I move the PTO lever aft to engage, the tractor dies unless I hold a little side pressure on the lever, it will then keep running.

What can I do to fix this problem?

 

[Katahdin]

When were the fuel filters last changed? Sounds like they're overdue.

 

[BeezFun]

Sounds like one of the safety switches, might be the seat switch if you have one. If you take weight off seat when HST pedal is anywhere but neutral the engine will die, so what might be happening is the seat switch thinks you stood up and wiggling the HST pedal keeps it running because it's in a neutral position. Ditto with the PTO. Most tractors will allow you to tip the seat forward and run the PTO so you can be on the ground using something like a log splitter. It's possible what you're doing when you pull the PTO lever to the side you may be leaning enough to put more weight on the seat so it doesn't think you're standing up, but haven't put the seat in the tipped forward position. I'd try jumpering the seat switch out completely to see if that solves the problem, if it does you can get a new switch.