Like most of the intelligent threads I haven't read this one too, thinking I'd get confused.
What I feel is that, Frodo on his journey goes through a lot. From the beginning he is told something that can go against him while fighting with the Ring. Elves would fade away if he destroyed it, and if not-- he'd doom the world. Did he give in? Yes, kind of... Or the Ring overpowered him? This is true as well.
When he was standing at the Cracks of Doom, he was wishing to destroy the Ring; but when he came upto the destined point, the Ring became more powerful than he was. He could not fight it as his Enemy was most powerful than anything; and he could not fight it because a). He was overpowered by the power that was more powerful than he was. b). He was weak--a weakness that everyone possesses and cannot be free of. c). He did something that did not require strength anymore.