People give away their labor in this case because it
makes them
feel good, and/or because of the non-monetary community rewards
surrounding the effort. Neither of those changes materially as
the economy goes down (or up).
Actually, a downturn in the economy would result in an increase in
unemployment which would probably result in more people with time on
their hands so more people doing volunteer work. It would also result
in big corporations having less money to spend. So, a downturn in the
economy is *good* for Wikipedia and the rest of Web 2.0.