Not familiar with this particular APU, but this is a pretty common baseline design. (basically a GTCP 36-150)
Primary fuel nozzles need cleaning. Uneven fuel distribution pattern out of the nozzle is snuffing out the ignitor and preventing light-off. First start of the day and after sitting a while the fuel evaporates and ignitor does it's job. But once covered in fuel it prevents spark.
Otherwise unplug the fuel shut-off solenoid and give it start a couple times. Listen for consistent 'cracks' from the ignitors. If it is only working part of the time may be time for new ignitors or ignition exciter.