The explanation was that the Lord of Light wanted him brought back. And eventually it stopped working. So, I suppose, it could work (though, she is likely to try it on Stannis as well, if she really believes he is the chosen one and true king).I was wondering if the end would be Jon opening his eyes as a wight. I mean, there is a certain character left out from the books who could be merged with that sort of situation. Although, my first guess was just that Melisandre was last shown to be at Castle Black (probably not a good place given Gilly's experiences), and she can always give the ol' resurrection thing a shot. We know that the other guy is the who who is capable of it, but maybe it'll work on someone like Jon... for... reasons?
The character you were talking about, in my opinion, is cut out of the show. Although, I guess technically, they do have a lot in common when it comes to Craster's camp. =)