20-Year Prospect
According to the Bureau of Laber Statistics, job growth for network administrators is projected at eight percent over the coming decade (source). That's about the average for all jobs, so no cause for concern there. In fact, the role of network administrator should rise much more in importance over that same time span.
Companies are still coming around to the advantages of a highly developed network and data infrastructure. The bigger the company, the more complicated all that becomes, and network administrators will be heavily relied upon to keep everything running smoothly.
It's difficult to project exactly what the changes in the job will be, because technology has a way of totally transforming job roles as new solutions emerge, but suffice to say network admins will be a big part of companies moving forward.