I'm not a carbon engineer or anything like, but I am a car enthusiast and the subject of carbon fibre does come up in the context of discussion about its longevity and stiffness etc.
Also on aircraft engineering forums with regard to things like the Carbon wings on the Airbus.
Summarising a loooot of contrary postings my understanding of it (which may well be completely misinformed and wrong) is that what we call carbon fibre is really two things, the Carbon fibres themselves and the substrate in which they are embedded, ie. cured resin of some type. The Carbon fibres give the stiffness, the resin holds them in place in relation to each other and "holds" the form in which they are shaped.
Two issues arise amongst those sceptical about the longevity and safety of Carbon fibre: a) whether the carbon fibres themselves snap invisibly and unawares within the the structure, one by one, until they no longer give the same strength to it; b) whether the resin / substrate itself equally gives up the ghost after a while.
Followed by c) which is the big unknown, is carbon fibre liable to snap and break unexpectedly and without warning after a certain period of stress ?
Alarmists say yes, supporters and Airbus engineers say no. By calling them the Alarmists I do not mean to denigrate their sincerely held views. I know an aero engineer who is absolutely convinced that neither he nor any member of his family will ever ever ever board a plane with Carbon fibre wing roots and wings. On the other hand there are the many very highly stressed military aircraft and satellite applications etc that have survived and continue to survive incredibly high stresses without falling out of the sky left right and centre.
Who is right I have no idea. But coming back to the OP's question, yes, it is possible that years of backward and forward bending of a carbon rod has caused a percentage of micro tiny fibres inside its structure to crack, thereby diminishing its resistance to bending and therefore test curve and "feel". It is equally possible that this is *******s....
That's all without getting into the further development of composite materials, which has moved on from "pure" carbon, to combine carbon fibres with kevlar fibres and other closely guarded industrial secret fibres (such as carrots) to comprise a mixed composite with all the best of each. Interesting field, materials, changing our world more than we realise I think.