First off I have been in a position where I thought that might have been the case for me, but as I have grown more and learned and understand more about the arts I realized that it was my own arrogance that lead me to believe I could have possibly caught up with my teachers knowledge or experience and understanding of the arts. So what I have done personally is let go of the idea that I could ever "catch up" and just maintain my study and effort to better understand the arts from my own experience and studies. And how do you "catch up" in rank? Seems that it would be impossible if you are following the time line? Although I myself have now that I think about it, he is still 2 ranks ahead of me and I have no concern with further or future promotion really.
So, what do I do? keep my nose to the grind stone and not concern myself with such things as they will not make me a better martial artist. And ultimately you can learn beyond your teacher but only if you are focused on learning and practicing not out ranking or knowing them in the first place. Just my opinion.

Hey Todd
Well In theory, it could be possible if your instructor stops learning himself so at some point you get so close that he can no longer test you himself. And the student instructors instructor need to test that student :) And remember just because you went the time between Rank does not mean that you get a new stripe on your belt but hey that is how I feel. Example my self is 1st 2009, 2nd 2015 and 3rd 2020

Believe me I understand, look at my time at 5th, not that I really cared because it didn't matter. I have a close (ish) relationship with my teacher, we don't really do a "student Teacher" thing on the mat anymore but we do discuss ideas and theories about the arts, and many times topics or themes from my book or system. The difference is that I am now at a rank I never imagined EVER and so it's a bit... Great discussion and I do see your perspective truly I do!

If the instructor stops growing and the student gets too close, he should seek a new instructor. As an instructor I guess one should be proud to have produced students that reach a higher level then yourself, but that's in an ideal world. In real life it requires a great man to accept that students pass you. I don't know how I would feel if that happens. I can only hope I'll be man enough to be proud of their achievements. It also depends on age I guess. If you're older it'll be easier I guess, because you can blame age instead of capability ;-)
But what if an instructor does have the quality, but just isn't interested in promotions anymore?

I believe I read a quote once that went something like this, "The greatest way to honor your instructor is to surpass him". I like the saying and have to agree with Marcel that it would require a great man to acknowledge and accept that. I am not saying it's impossible, not at all just highly unlikely for most to accomplish this. Great input and thread!

This is a real possibility especially if your instructor was a lower black belt to start and your lineage has minimum time and knowledge standards. There is a natural curve to learning in general, e.g. you learn a ton when you start (everything is new and exciting), belt mins are shorter, then you plateau, and the higher you go the slower the progression because you are working on intricate minutiae that takes longer to get. Finally, it matters how much time, and the quality of time, you are putting in and some people are naturally more gifted. There are high school teachers and college professors for a reason. At a certain point you can get into a situation where you aren't being sufficiently challenged and/or can no longer promote. Loyalty is important but it is a two way street, a good instructor should recognize this and ensure you are in the best situation to progress, doesn't mean you can't learn from or train with that person, but change is OK. It should be the goal for all instructors to make your students better than you! This is one of the benefits to having a lineage with a deep family tree full of great instructors at different levels!

I have been fortunate to always have mentors in Kenpo, but also in other arts. I have been allowed many times to explore other arts, and find what works for me. Sometimes my skills will surpass my Kenpo instructor in those areas, but I always stay respectful and share with him as he shares with all of us.

I guess, I look at it as a partnership, and want to share with him what I have learned, etc like he has with us.

I don't look at it as I am better, or have progressed farther or further, just simply I have worked things that perhaps work for my style of Kenpo, or my aptitude right now, etc, and we work together to make it other better etc.