A leak could certainly be possible. You could pressure test the system via a compressor and pressure gauge to see if it's holding pressure properly. If you notice that you are losing pressure, you could spray all the connections with soapy water to see if you can find the source of the leak.
I will say, that our water pump does the same thing, and the longer we use it, the less it happens as all the air is purged from the lines. Our water pump has a failed check valve though, so take that for what it's worth.