B&S 18.5 Twin Fuel? Problem?

My riding mower (9 years old) has a B&S 18.5 twin. After an hour, the engine shuts down and has trouble getting fuel. I have replaced the coil (thought it was a heat problem) and fuel lines (rotted) and do not know where to go next. The fuel filter does not stay full when this happens. I pull the choke a bit and remove the gas cap which lets the filter fill and lets me go 5-10 minutes longer. The gas cap appears to be vented enough.