I'd hazard a guess that the teeth on the rack inside the aerial mast have worn at the raised position.

The reason the motor continues to run on is that it looks to see a load

(when it's raised or lowered) in order to know that it's at the correct position and then shuts off.

As you nudge it, it drops sufficiently to re-engage the teeth of the rack with the pinion and then drive it down.

A new mast is about

£30-40 and not terribly difficult to fit.
