I do not normally start the apu in flight unless part of a procedure or my judgement calls for it. One of the reasons is that, as soon as I turn it on, I have one more possibility of a fire.
It looks like you fly NGs, so we're talking about the same apus here. If the apu fails to start on the ground, and as long as the FAULT light extinguishes after 5 min, you can give it a second try, while asking for a gpu during taxi in.
Now, if the place where you´re going lacks pneumatic capability that's a different thing, but otherwise, I just leave it alone in flight.
That being said, I don´t think there is anything wrong or unsafe with temporarily starting them in flight until a solution to the problem is found.
Regards,
SW.