Yeah and the sysadmins get paid well for doing all that stuff. Sorry, but I don't see the point in arbitrarily assigning extra gratitude for someone doing their job. If there's something wrong in that you're not properly compensating your sysadmin, one day of "appreciation" isn't going to change that.
People like knowing that someone cares for their work.
Therefore, there are some days for people who work hard but don't necessarily get a lot of recognition for it, because the work is mundane, invisible or otherwise unsexy. Thus, we get mother's day [1], secretary's day (in NL, at least), sysadmin day.
Of course, actually letting these people know that you care on the other 364 days is probably better than devoting one day a year to them, and there are more and more of such "days of foo" or even "weeks of bar". But the basic idea isn't that bad.
[1] Note that Mother's day has meant different things to different people at different times. Wikipedia has a - no doubt incomplete - overview.
But where does it stop? Do programmers get a day? DBAs? Testers? Business Analysts? Network Engineers?
All of these do things which aren't sexy and aren't appreciated (most developers don't spend their life changing the world, they're bug fixing and writing reports for the guys in finance). Can they have days too?
(And then the cleaner, the office manager, the interns...)
The point isn't that Sys Admins don't do good work, just what makes them different to everyone else.