Wow, you have had as many opinions as you have netted responses. 😀
Generally, if an exercise isn’t providing a training effect any longer or you’ve plateaued, switch to another exercise. Constantly stressing the bones, tendons, ligaments, and joints with the same activities and in the same way day in/day out leads to stalemating longterm. Manipulate lever length, grip, rhythm, tempo, direction, body positioning, and ROM to shock the muscles into continued growth as well as to provide more even wear and tear on the joints instead of always stressing them in exactly the same manner & with all the same exercises. This also keeps boredom at bay and keeps things fresh and different.
Changing a workout routine is based on goals. If you are pleased with what you’ve achieved maintenance may be the answer. If you want to continue to grow and adapt then mix up the F.I.T.T. What is your goal endurance, strength, or power? The answer to that will lead you to which F.I.T.T. component to change. As a general rule adaption to weight training 3x’s a week is acheived after six weeks, 2x’s a week after 8 weeks.
Periodization routines can cycle every 3 months with mini cycles within the three months. See articles by Len Kravitz PhD IDEA expert writer.
I usually change my workout routine for myself, and those for my clients, every workout. However, as for a general answer to your question I would say when EITHER, your workouts are getting boring/stale (i.e. mental staleness), or when you are no longer making progress (physical staleness or plateauing).
I wrote an article about this very subject that was published in a tennis magazine. If interested, I’d be happy to send you a copy, just email me.
I hope this helps.