change out the coil, install a hotter one, what I did on my to35, it starts better.
also when it stops running, is carb icing on the outside, take off your air pipe to carb from air cleaner, it might be freezing up, or your fuel line freezing up. do you run seafoam in your fuel or stalbuild?
could you have water in the gas? how old is you gas?
when it stops running take a sparkplug wire off and turn over motor, do you get a spark at plug.
if so, then its not the coil,
I am thinking fuel lines may be freezing up, then as it sets for a while, the heat from the motor thaws out the line stoppage
let us know what you find.
if new coil does not fix problem, I would drain out the fuel and add fresh fuel with seafoam.
check fuel cutoff for dirt you could have sediment in the cutoff filter and it will run so long, then stop up. I added an inline metal fuel filter, much better fuel filtration.
on my old tractor there is another fuel filter in the elbow as fuel line goes into carb, do not forget that one, if yours has that!!!!!!!!!!