I've looked into cf a bit.  It isn't really any harder to do than fiberglass.  Similar resins involved, just a different sort of fabric.

But I think that like any different material than the woods violins are traditionally made from, it would take a lot of experimentation to get the best sound from it.  The current traditional violin is the result of many years of evolution to get the body shape and curves optimal.  A new material would have different characteristics, and so just copying the math/curves/dimensions wouldn't be the best an instrument made from a new material could sound. 

Epoxy resins do have some problems with ageing.  But wood is also usually considered to have similar problems.  A 300 yr old piece of spruce isn't something you would likely want to use as a construction material in your home, for example. 

Epoxy does continue to change over time.  To get an idea what the long term problems can be, look at amber.  Amber is a similar resin, but with water removed as long chains formed over hundreds or thousands of years.  Epoxy is accelerated chemically to make it harden faster.  Not even a synthetic form of amber, it is basically amber where the hardening process was just sped up. 

The epoxy resin used in CF is probably going to be fairly stable over a reasonable number of years, but those instruments may not end up being something of great value over the course of centuries.  Mostly epoxy (whether used with CF or glass fibre) will have problems sooner if it is exposed to extremes or temperature or humidity, ultraviolet, or harsh chemicals.  So will wood, though.

Under the conditions most reasonable musicians will keep an instrument, hardened resins and anything (CF fabric, in this case) in their matrix will last quite a long time.  

Consider an antique violin finished with spirit varnish.  That varnish is largely resin that was accelerated by heat and then subjected to a solvent, applied and dried.  It is at least a close cousin in many cases to epoxy.  The finish on some of those violins is still nice after a very long period of time.

Fibreglass has a reputation for not ageing well, but the fibre itself is more brittle than CF, and where it usually doesn't age well is in things like boats and cars, where they are exposed to weather, sunlight, and lord knows what sort of cleansers and etc.  On the other hand, if kept away from such things (as music instruments usually are) I have seen fibreglass circuit boards (for example) from the 1970s that show no sign of ageing at all. 

40 yrs or more.  Well, that could be a very reasonable lifespan for a student grade instrument.  If it is reasonably stable and durable within that time span (or perhaps longer), it could be great.  For all I know, a CF violin might improve or degrade with age.  Nobody will know for sure until the first ones pass their first couple of centuries, eh?  LOL

But I feel the potential is there for some reasonably good sounding and playing instruments that could be of very consistent quality and more than durable enough for at least student/beginner needs.  I think in the end, most people will still eventually want the pretty instrument made of the traditional woods.  But low-cost reliable instruments with a reasonably long lifespan could definitely fill some of the needs of the music community.  They might not last for centuries, but they could likely last for a few generations of players.

On a side note, I really like how the fingerboard looks on the CF violin in the video.  LOL