Sounds like you may be losing fuel pressure. There is nothing mechanical in the fuel filter--You're probably hearing the pump. Put a pressure gauge on in place of the cold start valve and monitor the pressure. Fuel filters are cheap, so just replace yours (you can use a clear one before the pump, so you can see what is going on). I don't have a diagram, but fuel flows from the tank to the pump, is pumped through the lines to the fuel rail, is controlled by the regulator and flows back into the tank. Pressure should hold at 28psi if everything is working.

Another possibility is that your system is closed and you're creating a vacuum that eventually chokes off fuel flow, but i don't think this is the situation.

Rolfe
'71E