Whenever there is a topology change (a link goes down) on a switch other than the local switch, (an indirect link failure) then in such a situation, STP will reconverge in 50 seconds. This is due to the addition of the blocking timer, which is 20 seconds. Take a look at this post which refers to the blocking timer:
For a more comprehensive view of the reconvergence of STP, take a look at the following lesson: