I think that we'll need a bit more information in order to diagnose your problem. What sort of pressure pump do you have? Do you have a accumulator/pressure tank connected to your pressure pump? It could be that it has lost
internal pressure and will need pumping up. If you take the outlet hose off the pump, does the water flow to full capacity? If it is pumping slowly, it will take longer to get up to pressure and this might account for a drop in pressure after the first few seconds of using the tap.