The example doesn't really work since it's a hardware fault that probably needs the infant transferred to a new incubator (the fan in a normal incubator is not easily accessible especially while the infant is in there).
I expect it's not too hard to differentiate between conditions to decide when the 30min pause is OK. For example, modern systems usually have non-volatile RAM which can be used to tell the difference between a normal power off and a power interruption, and most systems would have real time clocks that can tell how long the interruption is as well as sensors to assess if everything has cooled down. With all that information, it shouldn't be too hard to develop an algorithm that makes sense, i.e. find the balance between minimizing false alarms while maximizing the alarm when needed.
It's not a perfect solution and even 30 min is a little arbitrary. The point is that simplistic software solutions such as power off (whatever reason) = cold condition = 30 min alarm pause would be wrong since there are low cost solutions that are better.
In reality, the audio pause is intended for warm up while the infant is not in there which is the normal way, you don't put the infant in while the incubator is just turned on). So an more ideal solution might be to use the incubators scales to tell if the incubator is empty or not
