I've been having a thought for a small prospecting ship, owned by a big-assed mining company. I was thinking about using the Intrepid-Class (from ENT), does it seem feasible that they would still be on the go by the mid-23rd century? I liked the design and fancy using it, but I don't want it to seem far-fetched that one is still on the go.
I wouldn't call it far fetched in the least.
Look at the current USS Enterprise aircraft carrier - 53 years old and built with 1950s technology, still actively deployed in 2012.
A starship built with 22nd century technology should easily see out a hundred years.