If the pressure starts good and then drops it not an issue with pump vs. shore (my coach I get better flow with the pumps on as I have 2 of them). You can disconnect the output hose of the pump and turn it on (point it outside or add a short hose). If the pump runs with plenty of flow, try blocking the outlet a bit to see if it still pumps well or the flow drops. If it drops you likely have a weak pump and it can be replaced or rebuilt. As mentioned you also want to check the filter screen if there is one and you want to check for any kinks in the line going from the tank to the pump. Even an old water line could collapse somewhat under suction. What kind of a pump is it and do you know at what pressure the pump is set? Does this happen at the sink as well as the shower when each is run separately?