It not your fuse box doing it.
The siren is not supposed to sound when the power is tripped, could you imagine the chaos if this happened to every alarm in your street in a power cut.
There is a battery in the bell that is designed to make the external sounder sound when there is no connection from the control panel. The panel is constantly supplying voltage to the external sounder, if it loses the voltage like when someone cuts the wire going to the sounder the battery then takes over and the sounder sounds.
The panel also has a battery inside, this battery keeps the panel powered in a powercut, this also means that the panel is able to keep the voltage going to the external sounder thus preventing it from sounding in a powercut. The fault you describe, your external sounder sounding in a powercut, there is something wrong, as above probably battery or battery fuse or charging circuit.
The sounder intermittently sounding is a symptom of the fault, not the fault, to test if the sounder is good, with the power on set the alarm off by aring it and walking into the armed area. If the sounder sounds as it should, then you need to get someone that knows what they are doing to take a proper look and make a proper diagnosis of what is actually wrong.