I had the very same problem with my 12.5 HP B&S on my Murray riding mower. It was the air filter that caused my problem. I thought I could mow one more time without changing it, but like you said, after about 10 minutes, it quit running and wouldn't crank again. After checking, I also found low gas and overfull with oil that smelled like gasoline. I changed the oil, put on a new air cleaner and had no more problems. Unless you've already replaced the air cleaner with a new on, it would be worth a try before taking the carb off and tearing it down.