Of course they do! Not only are we not immortal, our role as a mentor probably should be limited, or reviewed from time to time.
Actually I dislike the term “mentor” but let’s not get tied up in semantics.
One person bringing out the best in another would be a valuable activity. It requires trust on the one hand and expertise and experience on the other.
But why don’t people stay with the same “mentor” for ever?
Thankfully people grow and move on. That’s our job isn’t it?
If you could arbitrarily divide life up into stages, Stage One could be: helping a person discover just how good they could be.
Stage Two could be working with a person to discover what they want to be, now that they know what they are capable of.
Stage Three could be facilitating that person to lead others.