Bitumin, that engine is covered by the B&S engine overhaul manual:
http://www.tpub.com/content/recoveryvehicles/TM-5-4240-501-14P/css/TM-5-4240-501-14P_70.htmYou can use the Next button to get subsequent pages (there are 224 of them) or just overwrite higher numbers where the 70.htm appears at the end of the URL. You will find the carburetor diagnosis and repair for the larger engines such as yours begins here:
http://www.tpub.com/content/recoveryvehicles/TM-5-4240-501-14P/css/TM-5-4240-501-14P_114.htmI think your carburetor will be a large one-piece flo-jet or a two-piece flo-jet, depending on the year of manufacture.
The governor information for your engine begins here:
http://www.tpub.com/content/recoveryvehicles/TM-5-4240-501-14P/css/TM-5-4240-501-14P_138.htmIf you would like to discuss this repair process as you go by continuing this thread, please post the full model, type and code for your engine, which is stamped on the air cowl. We will then know the date of manufacture, and can work through the diagnosis and rectification with you, based on the manual.
In case we end up running a "who guessed it first" on this case, your symptoms sound rather like a fuel restriction upstream of the float bowl. It would probably be due to dirt that was intially in the fuel tank but may now be either blocking the seat at the entry fitting, or jamming the needle. I'm betting against Bob in this case: there seems to be a time delay before it conks out, making me think the problem is upstream of the float bowl. (I doubt that I'm right any more often than Bob is, by the way.)