... because shutting down an engine gives a MUCH bigger problem than shutting down an APU, which is only a minor inconvenience.
The chance of a fire occurring on the same flight in which a detector fails is so small, it is well within safe limits to continue to destination.
It would be so for the APU as well, however as the APU isn't
necessary there is a tiny improvement in safety by shutting it down.
If you are my FO, you can watch the nearest suitable sail by as we continue to destination ...
