Intel's research budget last year: $5.7 billion
AMD's Revenue last year: $5.81 billion
Intel needs AMD to exist so that they can avoid anti-trust lawsuits. If AMD fails then Intel will face a lot of legal problems.
Disclosure: My dad works for Intel.
We have seen many giants fall or fail, Microsoft never came up with an answer to the iPod, you may argue that MS didnt really try that hard, but still I think its a good example.
And finally, there is always a place for No. 2, AMD can be a player, it doesn't have to be No. 1 to remain a player.
EDIT: According to the article, AMD bagan to rock with server processors in 2003
That's a little optimistic on Intel's part.