Your water pump has a check valve inside that is suppose to prevent water from backflowing into your freshwater tank when on the city water hookup, and also hold pressure to all the faucets once pressure has been obtained while using the pump on 12 volts without city water. This could be the problem.
If you have no leaks present anywhere, the other possibility is that it's sucking air from the suction line that goes to the freshwater either through the line or the inlet screen on the inlet side of the pump. If you find nothing there, then it would be likely the backflow valve on the pump has some trash in it and is allowing a little water to backflow and once the pressure drops the pump will cycle shortly to regain the predetermined pressure.
In some cases you can take the pump head apart and clean it out. Sometime just cycling the pump off and on with the faucet numerous times will make the trash clear itself.