Small Engine Troubleshooting Problems? Ask a Mechanic Now.
Welcome to JUST ANSWER small engines, let me try to help you !! The fuel solenoid in the carburetor may be loosing its grip and is closing off the main jet in the carburetor. It has to stay open, with 12 volts, as long as the key is on. Best test is to remove it and plug the hole. Depending on which engine you have, this may not be possible! On Kohler, you may be able to remove the inner tip, that does the closing, and re-install as a dummy for test
I would not rule out a fuel pump. But the fuel filter will never show to be full when the engine is running. All small engines do the same! Just the nature of the fuel flow.