That is not normal, and could be causing harm to the unit by running that way. Sounds like a pressure switch opening and closing.
I did have an issue earlier this spring--after turning on the heat pump after it being off all winter (I have oil for the cold months)...I had a repair company out--they stated I had no pressure and recharged the system completely (9lbs). Also put is a dye to see where it was leaking. They came back two weeks later--the system pressures tested perfect, and they could not find any leaks using the UV light.That is not normal, and could be causing harm to the unit by running that way. Sounds like a pressure switch opening and closing.