I had the exact same problem. I found out that it had to do with the air cleaner box. I found out that the design of the air cleaner box didn't allow air into the carb. I removed the air cleaner box completely. I used a zip-tie to hold the air-cleaner(sponge) to the carb and the engine runs perfect and never stops until I release the safety bar. I only used this mower 4 or 5 times. I only owned it for a couple of months. I also noticed when I first removed the air-cleaner(sponge) it was yellow and looked brand new. The only problem was that it was super sticky. I'm not sure if B&S use some kind of engine cleaner/oil during the manufacturing process. But the filter was all sticky for no reason. I followed the instructions exactly when I first purchased the mower from Walmart.

I plan on buying a new air-cleaner box and new filter to see if this helps keep the mower running as normal. I used to have to prime the mower 10x then it would run for about 5min then quit. I would prime again to get it running again.