It MAY be a faulty ignition switch. It sounds, from your description, like the fuel pump is dying--which could be the OVP relay, fuel pump relay, the ignition switch input to the fuel pump relay, OR the fuel pump itself. If I remember correctly, there is also a RPM limiting relay in the circuit. The key symptom is that it will 'restart'. An ignition related fault would not heal like that but would stay dead.

I presume you have changed the fuel filter.