At least Techcrunch provided some reasoning.
Your prediction is worded in a way that makes it hard to argue with, because "relevant" is so subjective. I know a lot of artists find MySpace VERY relevant.
However, to attempt a rebuttal, taking the Facebook case:
If Facebook is to become less relevant than it is now I would argue it's growth would have to stop, or at least slow down. According to the linked article it is currently accelerating, and usage of Facebook APIs OUTSIDE of Facebook is increasing enormously.
Growth like that doesn't just stop, unless there is some external factor.
So far, Facebook have proven themselves to be reasonable technically skilled, so I'll rule out technical problems.
It's possible some kind of legal issue could slow them (privacy lawsuits or something?). However, lawsuits take such a long time to play out that it would probably be at least 2-3 years before any negative verdict against Facebook would make them change what they are doing, and even then it won't shut down the site. If Facebook have 2-3 years more sustained growth it would be unprecedented for them to shrink from half-a-billion users to something less relevant than MySpace in another 2 years.
Another good counter-argument is the likely-hood of an IPO in the next 5 years. Apparently, Facebook had $700 million in revenue last year, and should do $1.1 billion this year (http://www.insidefacebook.com/2010/03/02/facebook-made-up-to...). If they IPO'ed now, with a P/E ratio of 20 (Google & Apple = ~24, Microsoft = ~ 17), then they'd be a $20 billion company. That buys a lot of relevance.
EDIT: Note that is a revenue figure, not an earning (as pointed out below), so the numbers are wrong. I'll leave it here, though, because the point is more important than the numbers - if (when) Facebook IPO's they will raise a LOT of money.