Outdoor Power Equipment and Small Engines - 42e707 Running Problem

I HAVE A B&S 19.5 TURBO TWIN. IT WOULD RUN THEN DIE AFTER AN HOUR OR SO AND WOULD NOT RE-START FOR AN HOUR. I REBUILT THE CARB. AND IT DID THE SAME SO I PUT A NEW COIL(394891) ON IT AND IT RAN FINE THE FIRST TIME I USED IT. THE NEXT (2ND.) TIME IT DID THE RUN AND DIE ON ME.
CAN ANYONE TELL ME WHAT IT MIGHT BE?? I AM GOING TO REPLACE THE PLUGS, FULE FILTER AND AIR CLEANER TODAY BUT I DONT SEE THIS HELPING. THANKS FOR YOUR INPUT.:alarm:

With only a few exceptions, (and yours is not) valve seats are factory pressed in steel inserts. They press into the aluminum cylinder block and if the engine has overheated in the past or currently there is a possibility that one or more of the seats could dislodge ever so slightly and you lose the necessary seal between the block and seat. Not to mention you lose valve clearance on the valve corresponding with the seat that has dislodged. This could be your trouble since it appears you have a heat related issue and you've covered the other bases. One other heat related issue of possibility is if the cooling fins are plugged up thereby overheating the engine you could have a vaporlock issue with the fuel system.

Plugged cooling fins/overheating is what I'm leaning towards also. There are small tins on the bottom of each cylinder held on with a 5/16 head screw. Remove these and check the underside of the cylinder fins...this is a common area for them to clog. If they are clogged here, go ahead and remove the shroud and tins and clean them out completely.

Also might check the fuel cap vent to be sure it's venting.