Alas, this is one of those thorny issues where matters of perception can turn into matters of legality (age discrimination). That said, most network admins do indeed seem to be in their 20s and 30s if you look around in most mid- to large-sized companies nowadays. This doesn't mean, however, that you can't find a job as a network admin at your age; but rather that your years of experience translate into a longer lead time in finding new work. An old "rule of thumb" for finding work is one month for every $10,000 in annual compensation you seek; if you're looking to make more than $60,000, your time has not yet "run out."
My counsel is as follows: (1) Continue your search for network admin work unabated. (2) Identify a different technical area -- database, security, etc. --where you'd also like to work, and start training in that area. Either you'll get a job as an admin before you're trained, or you can start broadening your search once you are nearly trained. As long as you can afford the training or self-study involved, as well as the exams, you'll be able to pursue more opportunities that way.
This was first published in November 2002