We haven't had a person get the nomination of a major party again after being defeated in the top slot, for whatever reason, since Nixon in 1968 (and before that, one has to go back to 1956 and the second run of Adlai Stevenson).
The 'loser' tag that is so forcefully stuck by both the media and by party insiders is a mighty hard hill to climb. Not impossible. But pretty darn hard.
Let's take Gore for an example. He came within 538 votes and an incredibly bitter court fight of getting the presidency in 2000. Under this idea, he should have been a natural for getting consideration for the nomination again in 2004. Except almost no one in the party wanted anything to do with him at the time.
IMO in 2004 he would have had a
tremendously hard time getting the nomination if he had sought it. There was a large sized block of Democrats who blamed the loss in 2000 on his ineffectual campaigning. A sense that he threw away a sure thing as it were. Sure, the Blame Nader faction always got the most attention (unreasonably, IMO). But the movers and shakers of the party? They were
pissed at Gore at the time.
By 2007/8 he had more or less rehabilitated his image (his green crusade during the decade certainly helped in this regard) but by then there was a sense that his day had come and passed. Maybe he could have gotten the nomination by then, as his standing in the party had rebounded. But there simply wasn't room in the field for him. But perhaps in a TL with no Hillary Clinton and no Barack Obama, there could be a chance at him getting the nom.
A similar dynamic could envelope Dubya. There would be the noises that Bush had what would be perceived to be a slam dunk win and he let it slip through his fingers for whatever reasons could be imagined. Look at the current character assassination of Mitt Romney to see what I am talking about (though Mitt certainly isn't helping his own cause

). I can easily imagine the same thing happening as Republicans look for someone to blame for their loss.
By the time early-/mid-2007 rolls around (which is when the election season gets started in ernest) could George W Bush have repaired the damage enough to mount a serious run? Maybe. But the economy hasn't crashed yet (though there were plenty of warning signs) so he can't play that card.
It is possible I suppose. But he's either gonna have to lay the ground work around 2006 or so
or fight a lot of institutional forces that may be lining up against him.