The APU in the DH8 100/200/300 is not contained in a fire-proof compartment, therefore its use airborne is prohibited. If the APU was left running, when the nose wheel leaves the ground, the APU will auto shutdown.
I've seen an occasion when so much freight had been loaded in a DH8-100 rear locker that the APU shutdown. Enter 10ish folk to the flight deck to depress the squat switch and restart the APU. Darn thing shut down again when they left!
I'd be surprised if the DH8-400 was significantly different.