Your ball box obviously has a back up battery in it. Possibly it's ringing due to needing replacing - a sort of pre-total failure alert.
Most bell boxes have their own batteries to ensure that cutting the feed cables to it wont disable it or stop it ringing. The other possibility is that there is an anti-tamper switch in the bell box and there's a poor contact there although normally once tripped the bell would ring for the preset system time.
videoguy, October 2006