I think Ayn Rand left it up to the reader to decide Eddie Willers' fate. Did he die? Perhaps. Then again, it's just as likely he was able to make it back to civilization. The reader will never know, of course.
Why didn't Dagny or Francisco save Eddie? Good question, and one that will also remain unanswered. My own feeling is somewhat cruel: that Eddie simply wasn't in the same "league" as Dagny, Hank, Francisco, and, of course, John Galt. And because he wasn't, his life was not as valued as those others I mentioned. Suppose it had been John Galt stranded in the desert instead? Is there any doubt that Dagny would have moved heaven and earth to save him?
Of course not.
But Eddie Willers was...well...Eddie Willers. He wasn't exactly a loser, but he wasn't anything special either. He had the loyalty of a dog, true, but that was about all. A nice guy with not much to offer the world, in other words.
I think Eddie existed in Atlas Shrugged to show that even nobodies like him could be useful to the John Galts and Dagny Taggarts of the world, at least in a subordinate position. But that people like Eddie couldn't easily make it on their own without powerful people like Dagny and Galt to show them the way. That, perhaps, is the symbolic meaning of Eddie's abandonment in the Arizona desert at the end of Atlas Shrugged.