...However, we know that starships don't actually enjoy such a safe mode, not when it matters. Sabotaging of engines was enough to send the ship on a death spiral in "Court Martial", without dialogue implying that Finney would have used those engines to initiate
the spiral before completing the sabotage. To the contrary, Kirk first says he himself commanded the engines shut down for the time being (due to manpower shortage created by the hunt for Finney - the engineers had to beam down), and Captain Krasnovsky then worries that the orbit will eventually decay - to which Kirk responds that there's still some time before that happens, but apparently not years or even weeks. It's after this that Finney sabotages the engines, the ones that supposedly take lots of crew to operate even if only one man to sabotage. So it seems that parking a ship around a starbase planet for what's supposed to be an indefinite time (pending the outcome of Kirk's trial) doesn't involve using a stable natural orbit...
Then there are a couple of cases where gravitic anomalies or tractor beams are acting on the ship, but that's a different matter. It might be that every time the ship wasn't
sabotaged or didn't lose power, she was on a safe natural orbit. But that's statistically and dramatically a bit funny.