My original sport is ice hockey, and this absolutely happens to our carbon fiber sticks. While most of them break after a month or two of heavy use at higher levels (if not sooner), if they survive, they lose their "kick" or "whip". They flex under load, but don't spring back as a fresh stick would. As a smaller player who didn't load sticks as much during my career, I seldom broke carbon sticks, but I did end up with a pile of "spent" sticks sitting in my garage, haha.

Edit: On that note, hockey players who "know" will tell you the performance differences in terms of kick between the mid-grade and upper-end sticks is minimal, the difference is weight-savings, as top end sticks are feather-light. Interestingly, the prevailing wisdom is that if you want a stick for pure performance (weight+kick) you get top end, but if you want a durable stick with kick, go mid-grade.