Mower dies after 30 Min. of use?

I have a Briggs & Stratton Quatro 4HP mower and it dies after 30 min. of use. The last time I noticed the primer button was sucked in. I took off the fuel cap and wiggled the primer until it popped out to where it should be. It started up right away but died after 10 min. I go through the same routine and it starts again. It did this 3 times before I finished mowing. My question, does the primer ball need replaced or is it more than that.The fuel cap looks like the vent holes are clear. No problem with running hot or fuel leaking. New spark plug and cleaned the mag and adjusted it. Any help would be appreciated.