I think the obvious answer is "When you start asking if you're too old to watch anime". Ba-dum-dum.
Obviously Vexx and Furudanuki don't feel like they're too old (and either one is as old as my father ... so that tells you something). I, for one, actually find good shows on American TV (apparently, in the immortal words of Beavis and Butthead, I get the one channel that doesn't suck) - so I doubt I'd ever get burned out on anime because it doesn't make up a huge portion of what I watch and/or do. If it's the only thing you're doing then I'd expect you'd burn out at some point - that's what happens to most people when they obsess over something.
