What are the long term material properties of VeroWhitePlus 3D printer material?
In our experience, the parts will continue to cure. I don't have the chemical science background to provide proof or evidence, but I operate from an assumption that if the part requires UV rays to cure, it will continue to be reactive to UV rays after it is considered "cured". 

I too have found the same brittleness over long periods of time. The only experience I have with the moisture issue would be a small component designed and built for a cable pulley in the tail section of an aircraft as a temporary solution (acting on a non-critical trim control surface). The aircraft is based down here in Houston, Texas where we get some pretty gnarly humidity. The part did begin warping after a few months but we don't have definitive information indicating it was a moisture problem, or something more structural. 

I do know however, that if you aren't absolutely meticulous about cleaning ALL of that gelatin-like support material off of the part, it does wind up being more susceptible to slight deformities, and when you DO remove it all thoroughly,  it is then slightly more susceptible to the brittleness issue. Not sure if I'm the only one finding this, and apologies for not having the chemical background to provide more quantitative support.