If there is no obvious leak (no water in bilge, no wetness at connections, no faucet dripping, etc., the only place the pressure can be going is back out the way it came in.
Our systems have a one-way check valve located between the water pump's impeller and the fresh water holding tank. Typically, they are part of the pump itself, located on the inlet side of the pump. These check valves keep the pressure that the impeller builds into the system from bleeding back into the holding tank.
Once enough pressure pushes backwards through a faulty check valve, the pump senses the drop in pressure and re-pressurizes. No water is being lost, hence the difficulty in finding an outward leak... because the pressurized water is simply going back to the holding tank.
Unfortunately, I personally don't know if these check valves are a replaceable item on the pump... I would imagine it would be, but I can't speak to that. But many times, the check valve consists of a rubber diaphragm that sits against a 'cage'. If sediment gets lodged in the cage, the rubber diaphragm can't sit properly, and water can push past it. So, it might be more of a 'cleaning' situation instead of replacement. Taking the pump out and trying to flush the inlet port out would be my first option.