Whatever could be causing it to not maintain fuel pressure. That could be a restricted inlet, restricted outlet (kink/bend in the supply line), a bad pump, bad wiring (voltage drop - could be on either the power or ground side), probably not a regulator since it's at its highest demand with the least amount of fuel consumed by the engine...
Just to be clear, nothing you do should be able to make fuel pressure drop more than 5 PSI. Ever. Under any condition.