I have a craftsman self propelled mower with a briggs and stratton 6.5 hp motor. The other day when I was starting it, it would run for a second or two and quit. Pump the primer again 3-10 times and retry...same thing. Eventually I kept pressing the primer bulb and the mower ran and I mowed. This week I went to start it and noticed the carb was loose. Pulled it off checked the orifices for gunk and reinstalled. The air cleaner was embarrasingly filthy, knocked it out and tried to start it. It runs, doesn't surge or anything, but when it hits grass it has no power and eventually dies. Again, pressing the primer bulb breathes life into it.
I am a fairly good car mechanic and handyman and pride myself on being able to fix most anything, but for some reason the simple small engine always throws me for a loop.
Sounds like the air/fuel ratio is lean. There are a number of reasons the A/F ratio could be off - leaking gasket/O-ring at carburetor to engine mount flange, partially plugged main jet, improper mixture screw adjustment (if applicable). Many times the gasoline that sits in a small engine over the winter months will evaporate and/or congeal leaving behind a mess that causes the problems you describe. I'd start by removing the carburetor and do a complete disassemble, inspection and proper cleaning of all components involved.
Sounds to me like it is time for a good tune up. If your air filter was clogged it will lead to premature spark plug fouling. I would change or clean the plug and filter and also get so carb cleaner and clean the carb.
Also..you mention that the carb was "loose"? if your carb is or was loose it will cause the manifold vacuum to draw in fresh air instead of air through your carb thus resulting in loss of power. http://www.practicalconsumer.com/lawn-garden/push-lawn-mowers/