Sounds like an electrical problem. If the fuel gauge is showing less fuel when this problem occurs you either have a short in the wiring, bad ground, or a lose ground somewhere.
The electric fuel pump is probably losing power when this occurs, which then requires the injector pump to suck fuel. This pump is not design to do this and therefore causes a drop in engine power.
Also there is a small fuel filter in the bottom of the electric fuel pumps, most people don't know this. I would also check that filter, not that will fix your problem but they tend to plug up with debris from the tank. There is a nut attached to the bottom of the fuel pump that you turn just a little way to get loose, it is a cam style lock not threads.
If the filter is plugged, it could cause the pump to overheat and temporialy short out until it cools down.
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