User blog comment:The Milkman/Extended Expectations, Part II/@comment-4835791-20120628111039/@comment-1221773-20120629075718

If restoring EDI was at all possible then I think we would have seen an inkling of it in the ending scenes. The fact that we do not (and instead see EDI's name on the memorial wall) speaks for itself. Even if EDI did survive/could be fixed, that implies that other synthetics, most notably the Reapers (whose code EDI is based off of), could recover as well, which renders the entire Destroy option pointless.