Does carbon fibre go "stale" ?

I've never heard of it going "stale", but it gets really weakened if it took a huge hit.

no.

If properly constructed, it should be sealed from any air contacting the actual carbon. The clear coat may fade with age but the carbon isn't affected by atmospheric aging as long as the outer layer isn't scraped away. Taking a nasty hit, thats another story.

It does actually weaken under prolonged UV light exposure. However most carbon products contains some sort of UV blocker

As far as I know I don't think the carbon itself gets weakened or damaged at all with age. The problem can be the resin that holds it together. I supposed certain enviromental conditions could degrage it and I think thats the part that's really susceptible to UV damage. As a rule I would not recommend buying used carbon parts you don't know how were used, particularly high stress parts like handlebars and posts. Any used carbon that is particularly susceptible to clamp damage is a big no no for me. They could have unseen fractures and damage or maybe simply worn down integrity of the resin and fibers due to use.

correct, it is the resin that degrades in UV light.