I'm with Gremlin on this one.
As the car is getting very little use and possibly short journeys, the battery is not getting a sufficient charge.
Just starting the engine alone takes a huge amount of charge form the battery, several hundred amps! Plus I assume the hoist has a very large motor.
A new battery will only solve the problem short term. Have you got a battery charger? If not, it could be a wise investment. An overnight charge now and then and before using the car should cure your problem, and as Gremlin says, keep the engine running while using the hoist.
B-Max Titanium 1.0 125bhp manual City Pack.