The growth rate and kill rate of the cycling bacteria are slow compared to most of the rest of the bacterial world. The bacteria will die off at about 10% a day without food. I.e. if there are 10 million when you done, in 1 day without food there will be about 9 million, then 8.1 million after two days, etc. This assumes you are keeping them wet and at normal tropical temperatures. They will also be sow to grow, so if you wait more than 1 day to put fish back in, there is a possibility of a mini-cycle as the bacteria change from "hold on as long as possible until starvation" mode back to "grow" mode.
The completely technical answer to your question is 0 seconds. The die off begins immediately after the bacteria are stopped being given food.