Tigole just posted in the official forums that upon Wrath's release, the bear will be replaced with "a very good, epic item," basically to preserve the prestige of having gotten the bear at its intended difficult level. He says they plan on doing a similar thing with the "Hand of A'dal" and "Champion of the Naaru" titles as well. I can understand this move -- it would probably be trivial to get the bear with a raid full of level 80s. And there is still a fair amount of time before Wrath comes out.
However, it makes me sad to see something become impossible to get. I think it would be a better solution if they made it so the bear could only be attained by a raid containing no members above level 70, personally. As Zach pointed out to me, the change that they're proposing now means that no Death Knight will ever be on a bear mount, and that's just sad. Unless, that is, they introduce a polar bear mount in Northrend -- did somebody say panserbjørne?
If this is one of your goals before Wrath, don't forget to check out WoW Insider's complete guide on how to get your own Amani War Bear.
Update: Chances look good for a bear in Northrend. Tigole said: "Polar Bear sound cool?"