Why can't Roy Mustang bring his eyes back using his gate?
In the final chapter of the Fullmetal Alchemist manga, Roy Mustang said "I'd readily sacrifice my own gate like Fullmetal did, but then I'd have no way back".
Why he couldn't come back like Ed did?
I'm not completely sure if my answer is any good, but I feel like it was worth putting this out.
We do indeed see that being blind would have prevented Roy from staying in the military (according to the manga), and that in theory he could have regained his sight by giving up his gate. But as pointed out in the question he would "have no way back". This doesn't seem to be related to the fact that his responsibilities as a state alchemist might be affected if he took that route, particularly when we see Grumman, who isn't a state alchemist, become the Fuhrer (although he admittedly is a lot more experienced). Rather, I interpreted it as follows:
Ed's gate has some sort of connection to Al's. We see this when Ed ends up in front of Al's gate (after he is swallowed by Gluttony) and sees Al's body. It's thus possible to conclude that Ed can "exit" via Al's path, instead of his own. This was stated to probably be related to the fact that they both put in blood into the mix of ingredients used in their human transmutation attempt, somewhere probably midway through the seres.
Consequently, Ed can give up his alchemy without being unable to escape the realm of the gate, as he has two possible exits (Al's gate, and his own) prior to giving up alchemy, and giving up alchemy only means giving up one of them.
Comparatively, Mustang hasn't had an experience akin to Ed and Al's - he does not "share" a gate with anyone. He can only enter and exit the realm of Truth through one means, but since it seems that entering (and presumably exiting) rely on there being a Gate, he would be unable to leave that place if he gave up alchemy (and consequently, his gate).
This is just a supplement to Maroon's answer which is far too long to be a comment.
In the raw manga, the original text is not akin to the English phrase "to go back" (as in, to return to the way things used to be; the metaphorical sense). It actually is a literal remark that he will be unable to return [to the real world] after destroying his gate.
「鋼のがやったように自分の扉を通行料にできれば良いのだが帰りの通路が無くなる」
Which translates somewhat more literally like,
If I could, I would do what Fullmetal did, and use my gate as the toll; but then, the path for me to return home would disappear.
Additionally, the reason Edward was able to give up his gate is, as Maroon said, because Ed and Al's gates are somehow connected. After Edward destroys his gate, he turns around and Truth points him toward Alphonse's gate, where Al is sitting. The two boys return through that to the real world.
Since Mustang could have done no such thing, it makes sense he would have concluded there to be no way to return once he had destroyed his gate.
Note: Please don't accept this answer; it's just here to support Maroon's; if you agree with it, please accept that one instead.~
In the final episode of FMA: Brotherhood, a montage of everyones included Colonel Mustang with a thin mustache and a short haired Riza Hawkeye. Notice that his eyes aren't grayish anymore. They were black and it seems like he got his sight back. Mustang agreed to have Dr. Marcoh heal his vision but only with the condition that he tend to Jean Havoc first.
