B&S lawn mower stalls

My Briggs & Stratton Quantam XRM 6.5 hp engine on a Snapper body stalls out. I prime the bulb 5 times, pull the rope and it starts right up. No sputtering, no coughing, no shaking, just smooth running. It lasts for just over 1 minute and then it calmly dies. If I prime it again, it will not start. I did it the next day and the same thing happened. I did not have the time to try to see how soon after dying that it would start. I have done this three times now. Had not had any problems with it previously. It was left out in a light rain for about a half an hour to an hour a few days before this started happening. Any ideas?
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First thing to try: Loosen the gas cap and see if it still does it. It sounds a bit like vacuum lock of the fuel system. If the loose cap fixes it, find the pin hole on your cap and clean it.
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Second thing to try: pull the air filter - will it run without it?
-- Oren
..through the use of electrical or duct tape, achieve the configuration in the photo..
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