If adherence is a problem, changing exercises can help, otherwise there are no fitness-related benefits.
The idea that we can be too well adapted to an exercise to obtain a benefit is simply unsupported by any evidence. Muscles become stronger, for example, when they adapt to a higher level of resistance, not when they adapt to a new exercise. Repetitive-use injuries are better addressed by maximizing the efficiency of your workouts or by adjusting your workout schedule.
Here’s a simple example: Let’s say you want to improve your upper-body strength. How would you measure it? Most people think that the bench-press is a good indicator. As far I know, there’s no evidence that doing anything else other than progressive resistance training with the bench-press itself will maximize your performance. (You might get some benefit from training individual muscles, but the improvement will come from increasing resistance, not from adaptation to a new movement.)
So, I guess my answer to your question is either “never” or “as often as you like”. 😉