GoodByeBuddy is a free Twitter bot account that notifies you with a direct message whenever someone unfollows you. To start using this service, you just need to follow GoodByeBuddy on Twitter. Once you do that, GoodByeBuddy keeps monitoring your followers on frequent basis. Whenever anyone unfollows you, GoodByeBuddy sends you a direct message with name of the Twitter user who unfollowed you.
GoodByeBuddy is a completely free to use service. It does not needs your Twitter credentials to monitor your followers, and by sending direct message ensures that this information is not publicly available. This is a very practical service to find out whenever someone unfollows you.