You have checked the non return valve at the foot of the pump to make sure it is not leaking and allowing water to flow backwards back through the pump? This would make the pump start and stop all the time just as if you were drawing water from it in the normal fashion.
I have struck this problem a few times and it may be worth checking out at your end. At the end of the day it is just another dang thang ya gotta get right with a pumped system – bless their cotton picking souls!!!!!!!!
Selgas Services Ltd
Craftsman Gasfitters, Plumbers, Electrical Service Technicians