Ha, feel your pain there! You should have the big plastic tank on top of the engine, right? There IS a fuel filter under there! Change it out! On the bigger tanks (9qt? IIRC) as used on most, the fuel filter is actually the entire white 90degree fitting/joint (with 1/2" inlet and 1/4 out) If you still have problems with it bogging down ~30seconds into use, I'd check out the fuel pump mounted on the side of the engine as well. Although the tank is over the engine these aren't gravity fed, fuel goes to the vacuum operated pump first. The engine may be running fine until all the fuel that was in the carb bowl is used up and the pump isn't working right/keeping up to fill it. A bad coil can also cause cause issues with sputtering/backfiring and loss of power, normally once the engine warms up. Next time it happens, pull and reconnect the plug boot on each side as it is running, one at a time. If one side made little or no difference when unplugging, bad spark with that cylinder.