Toro Recycler with Briggs 6.75 won't restart when warm

This is a 2010 Toro Recycler with a 6.75hp Briggs engine. Starts fine when it's cold and runs good, but just doesn't want to restart when it's warm. It's my father's mower and he has had this problem since last summer. So he took it back to the place he bought it from and they supposedly cleaned the carb and thought it was ok, but it's not. I brought it over to my house and took the carb off and took it apart. Pretty clean inside but I cleaned all the passages anyway with carb cleaner and blew them out with compressed air. I didn't notice anything wrong so I put it back together and back on the engine.

It started right up with one pull and ran great. So I let it run for about 2 minutes and shut it off. It restarted again, but not as easily as the first time. I let it run for about another minute and shut it off again. This time it would not start. So I shot a little gas into the carb and it fired up and seemed to run ok. But every time I shut it off I'd have to do the gas squirt to get it started again. BTW, this carb does not have a primer bulb. The auto-choke was closed when cold and then fully open by the time I ran it for about 4 or so minutes.

Any ideas?

Jags