Great teachers don't stay the same. And they have a teaching window that starts wide open but gradually closes. They may still have students when they are eighty, but the gap in that window will be open only a hair–if that. It's not that they become too old to teach; it's that their students are too young to learn.
If you study with an instructor when he is thirty, you won't get the same experience as when he is forty; at forty, not what you get when he is sixty. Because, assuming he keeps on learning and improving, the teacher won't be the same. The menu will be similar, but the food will be cooked and spiced differently.
Here's what I mean:
Once students becomes adept enough to begin teaching on their own, there is an arc that will apply to most of them. It goes something like this: A young teacher has a certain amount of technique and enthusiasm. They tend to be physically fit, as strong and fast as they are going to be, and a lot of what they will show students will rely on being physically fit and athletic. Look at Bruce Lee, who died in his early thirties. Guy trained four hours a day, was always in shape, and was formulating his system. What he taught mostly works only if you are fit and strong and fast. That's because he didn't live long enough to need old man moves.
Just for numbers sake and purely arbitrarily, let's say this age is from 20-35 years.
After a time, and how many years this is will vary, a teacher becomes smoother and more adept at what he or she knows. S/he internalizes the art, adjusts it to personal preference, and masters aspects of it so they become automatic. There may be other influences coming in, other arts, or more instruction in the primary one, and these are blended into what he or she knows–and for the sake of brevity, I'll just use "he" from now on–and the new stuff is passed along to students who are capable of understanding.
Let's say this is from age 35-55.
If a teacher continues questing for better ways, he will start to see patterns and ways of moving more efficiently. He may see other arts, or pieces of his own art he didn't focus on before, and figure out ways to assimilate and blend those in. Technique tends to fade into personal zen. While his physicality can be mostly maintained, there will be a drop in pure strength and speed, the nature of growing older. To counter this, a competent teacher will begin to compensate. His circles will get smaller, i.e., he will shift to more efficient ways of doing the same thing, those that need more skill, but less power.
From, say, 55-70.
After this, the teacher's skill, if it has been improving, will be of a level that his efficiency of movement is much finer, but his physicality is necessarily less. Much of what he does will be difficult, if not impossible, to show to beginners, because they won't have the ability to understand and utilize the material. Think of it like teaching a first grader to read, but the only material you have to do it is the Essays of John Locke–the material will simply be beyond their ability to comprehend.
This is why the window has narrowed. The pool of potential students has vanished–those students with the capability to see and understand the moves at this level will already be on the path and working through their own transitions to get there. Not to say they might not pick up a thing or two, but they will get it on their own if they keep going.
At this point, new students can't understand what the teacher knows. Adept students who can understand don't need him to teach them.
At different times in your life, you will need different teachers. Finding the right one at the right time is the trick ...