[weikel]

Well actually if they lost it they couldn't destroy Sauron( well leaving him a weak malignant spirit in the wilderness) the way they could by destroying the ring. The thing they could do is use the eagle to get them to mount doom and dump it.

[paul544]

It has often been speculated why the eagles never took them. It was something Tolkien, as far as I know, was never asked. The obvious answer is the same as 'why didn't they just take horses?', Sauron would be on the look out for such things.