from a functional perspective. What events can occur if the guy is not there? Now what will it take to fix those events. What costs? What type of man power? What special skills?
Try to list it all out and assign (guestimate) figures and then double those numbers. Include lost productivity, downtime, skillsets, # users affected, vendors, customers, and so on.
I am sure we could build quite a large list of issues that would be influenced by your Net Admin being gone. Think in terms also of what the guy does currently and how you/your department/etc are affected/benefited/etc.
Again, highlight the pros and cons. With cons make sure to tack on the $$$ (guestimate) that will cost the company.
This is the only thing I can think of that would get the person kept. Oh and is he working on any critical projects right now that would go "red" if he wasn't there. That's another one.