Dexter shows no signs of "going sane." More likely, he's been more sane all along than he gives himself credit for - his self-image as a "monster" is just a way he denies his emotions. But his mental stability is not going to get any better unless he starts making attempts at improving it, and he's shown no inclination to do so.
For him to do so would undermine the core of the story, the radical notion that Dexter is okay has he is
, and the ideal solution is for others to come to accept him (as depicted in the fantasy-parade in the S1 finale). If he has to change, and go sane, to make others accept him, that betrays the whole point of the story.