And the answer is:

>! Surprisingly, it's 1, that is, it's the same as if nothing happens when the ants collide, and this doesn't depend on $n$.

Explanation:

>! The phrase that says you're watching a particular ant is just a distraction so that people will think that there is complexity in this riddle, while in fact it's very simple. When two ants collide and each reverses its direction, position-wise it's the same as if each ant simply continues moving in the original direction. So the maximum time is when there is an ant at on end of a stick facing the other end. Since the maximum time an ant can be in the stick is 1 (from one end to the other), therefore by time 1 all ants will already fall off the stick, including the particular ant that you're watching.