Mark

APU with a building history of bleed air failing after short run times. With APU bleed inoperative.... no air is available for engine start, A/C pack operation, or Air Driven Pump (ADP) hydraulic power.

The absolute first place to look is at the gasket located between the APU air sensing pallet (or module) and the APU case (just outside of the compressor section).
  
     
  
The air module has several sensors mounted on it. It is changed as an assembly. Two of the sensors have long tubes that extend into the case. One for sensing compressor inlet pressure and one for outlet pressure.
  
     
     
  
If the gasket is missing (in our case) or torn, ambient air is pulled in which screws with the pressures seen by the APU ECU (Engine Control Unit). If the ECU cannot verify proper air pressures.... it shuts it off.