The same (I think) as if it was a new alarm. So if I had a battery fail, it would beep for the normal length of time while I am in the flight screen, and then stop as usual. Then it would occur for that amount of time again whenever I entered then exited map view. Then it would continue in that same manner even on different crafts without failures. The tone would play when I exited the map view even if no part had failed.
I can reproduce it by manual failing a battery on any craft while in orbit, then switching back and forth into map view. No 'mute alarm' option is available. I'm running a tonne of mods though, so if it's not happening on your end then I will give it a test with only dangit installed.