My guess is that this is a reference to shut-down/startup restrictions related to the shaft bowiing problem.
Correct. The BA780/! has a 1hr 15min gate stop. The rules with the APU cooling cycles don't leave any leeway if you shut it down.
Over on T5 (at ARN) we shut down the Qatar B787 APU, but that has around 2 hrs gate time and it works OK.
B787 must have two 90KVA GPU at the fwd connections at all times, or you get load shedding. It says in the book that you can start one engine with two GPUs, but we haven't tried yet. The APU easily starts both at once.