As long as chess can't be calculated from beginning to end, it is very hard to scientifically prove an opening to be refuted (aside from lines that leave you with such hopeless situations like a bare king against king and rook, of course).
If you are satisfied with a less scientific proof, I'd say gambits are even less so refuted. In my opinion, nearly all gambits are playable, as long as you won't play it against a superhuman database/program or a world champion. In a practical sense, probably no gambit worth of having a name is refuted in the sense of not being playable. Even if a gambit is widely considered unsound and often results in a worse position, it might contain enough steam to give your chess skill ample opportunities to overpower your opponent.I even remember a game where I suffered terrible against the BDMBDG because I didn't foundfind any refutation over the board. I only won because my opponent terribly misplayed the late midgame, but from the opening point of view he should have won the game.
So my answer is: No gambit I know of is refuted to the degree of being unplayable.