Small Engines (Lawn Mowers, etc.): eventually quits running, hp briggs, gas fuel

Question
I have a 22 hp Briggs, it will run good for about 5 minutes and then act like it is running out of gas.  Fuel filter is new, fuel pump seems good.  I noticed the area where the 2 wires plug in under the float get hot, could it be this assembly malfunctioning and not allowing the float to open?

Answer
Justin

The 2 wires under the Float are the fuel shut off so the engine does not back fire. This solenoid may be bad causing the fuel to shut down when the engine is running. When you turn the key on you should hear a click from the solenoid if you don't then get a new one.