I had actually avoided the APU auto shut down scenario intentionally so as not to muddy the waters. Auto shut down of an APU is more likely to be a nuisance to the crew than a safety issue.
I am assuming that the OP works on gas turbines in a marine environment, where having a control system capable of carrying out an auto shut down of the engine, if certain parameters are exceeded makes sense and is not likely to create a major safety issue. The turbines in these installations will tend to be running for more than a few hours at a stretch and auto monitoring will alleviate the need for someone to be tied to a control panel/terminal 24/7.
This clearly is not the case with aircraft where the crew, and not a electronic nanny, must be the ones to decide when it is safe and appropriate to shut down an engine.