I don't believe that age per se is a factor - it's about what comes with age and can't be denied or (often) remedied: lack of time, other responsibilities and calls on discretionary spending, injuries, wear-and-tear, and so on. The skater and the coach have to work with those limitations, not against them, and have realistic aims. Small steps can climb a high mountain - although possibly not by way of a triple axel!
Here's my experience (from a dance persective rather than a freeskate one): I'm now 47, not a natural athlete by any means
, and am a test skater rather than a competing one. I've recently squeak-passed the Foxtrot (which I believe is found at pre-silver dances in the USFS system). When Coach and I were goal-setting at my next lesson after the test, we both assumed that if my body holds up, hard work and time will get me through the rest of my current level - hopefully at better than squeak-passes! Three years ago, there is no way either Coach or I would have made that assumption. Baby steps have worked.
To my surprise, my faint ambition "to finish out the Senior dances if I don't die first" wasn't pooh-poohed by Coach - she actually admitted I've passed higher than she ever expected me to, and said "Who knows how far you can go? Let's keep going until you have to stop!" (insert long pause while she mentally went through the dances...) "We'll need to find someone to partner you through the rhumba though - my knees have given out." I did point out that the rhumba is about 20 years away at my current rate of progress, so maybe one of the current crop of kid skaters will be available to partner the oldie for that test!
Her comment about her knees, though, is right on point - they no longer work as well as they did when she was younger, and she has to work within that limitation.