It would take a highly specific set of circumstances, but it could happen:
a) Mitt must overperform on Election Day.
b) Mitt must win the popular vote.
c) Mitt must lose the decisive state by an extremely narrow, Florida-2000/Minnesota-2008-esque margin.
d) The Republicans should be successful at painting Obama's victory in the key state as fake (this one should be easy enough, when it's that close that's what everyone assumes anyway).
e) Obama's second term must be viewed by a solid majority of Americans -- 60% is the minimum -- as a failure.
That is, if Mitt is seen as the 'real winner' overwhelmingly, like Gore was, and there is a good deal of buyer's remorse about Obama winning come 2016 (like there really wasn't in 2004 with Bush), than Mitt could really run a legitimate campaign for the nomination in 2016.
It would take every bit of that for Mitt to ever be a credible candidate again. Even with those circumstances, Mitt would be viewed as a guy who blew an election he should have easily won. Mitt is not popular among Republicans and if these circumstances occurred, it would galvanize Republicans to view the victim of the election as the GOP as a whole, and not Mitt Romney personally. I believe that Mitt Romney, if he loses, will fade into as much obscurity as a former major party nominee can possible fade to.