Whenever I start the engine, I tap ‘Log Engine Start’. When I start to taxi (from hangar to apron) SD automatically starts counting the off block time. When I stop on the apron and let the engine warm up, the off block time counter stops counting, restarting to count when I taxi to the holding point.

That's right. It stops counting because if you remain stopped, that was the correct time. As soon as you start, it knows that wasn't your final stop so keeps going from where it left off.