ComplicationsSince Akihiko and Mitsuru didn't actually become a couple, there is obviously a chance they never would even if they didn't date the protagonist. Further, there are possible reasons why they would never become a couple even after the events of the game. There is no doubt about their relationship having a strong foundation. However, the purpose of this page is to look at some of the things that could prevent their relationship from becoming more intimate both during the course of the game and even afterwards.
From the point in which Akihiko and Mitsuru met until after their original Personas give rise to their higher ones, they are both in places in their lives where they aren't able to become intimate with other people. They keep others at arm's length and don't let on what their true feelings are. In fact, they probably aren't even in tune with their true feelings. Both of them gave up being close to others in order to focus solely on obtaining their individual goals. Neither Akihiko nor Mitsuru are shown to have any real friends besides for each other and Shinjiro, for example. Further, during his social link, Akihiko tells the protagonist he never thought he needed or wanted a girlfriend. Similarly, Mitsuru informs the protagonist she didn't have the time to give to someone else in a romantic relationship and therefore couldn't have a boyfriend. I would argue that Akihiko and Mitsuru are as close as they can be in light of both of their similar mentalities--which is why they seem to have a strong bond despite not being overtly close. However, if neither of them are thinking about or in a place where they could have a significant other, clearly forming a romantic relationship would be hard. It's already impressive they formed a strong bond given these conditions!
Of course, though, there is the argument that the protagonist opens both Akihiko and Mitsuru's eyes and changes their mind about wanting to be with someone else. If (s)he could do that, why couldn't Akihiko/Mitsuru? Realistically I would like to say it's because of the dating feature of the game. However, there is a chance that what Akihiko and Mitsuru are looking for in a partner is not what the other has to offer. There are also a few other reasons I can think of to explain this:
1. Too much time has passed: Everyone likely knows the stereotypical story where a guy or girl falls for their best friend but the other person just can't see them that way. In other words, they've been "friend zoned." Perhaps Akihiko and Mitsuru fall in this category. They've been friends and companions for so long, they just don't consider each other as being "datable."
2. Their personalities around the opposite sex: It doesn't take long for the player to see both Akihiko and Mitsuru are relatively awkward around the opposite sex when they realize they like someone. If you mix in the fact that Akihiko is intimidated by Mitsuru (he says Ryoji has guts for asking her out, after all) and that Mitsuru feels she needs to carry out her duty to the Kirijo Group by marrying her fiancé, neither of them would make a move even if they did realize they had feelings for each other!
3. What they like to do in their "free" time: If you compare Akihiko and Mitsuru's social link, the protagonist isn't exactly a spitting image of Akihiko or Mitsuru. Akihiko spends his time working out and training while you can't even spend time with Mitsuru unless you are a genius and get the highest marks on an exam. Akihiko does well in school and Mitsuru participates in fencing as a sport, but I can't really imagine them going to the library together to study or going for a run in the morning. That isn't to say they couldn't branch out or they have to have the same "hobbies" (for lack of a better word), but it would certainly help make spending time seem less awkward during the "hey we're dating" phase!
One last complication I've seen in a lot of fan fiction as a plot point is Akihiko seeing pursuing Mitsuru as pointless because of his own status/class. Mitsuru is next in line as the leader of the powerful and world-renowned Kirijo Group. She is obviously rich and has power. Akihiko is just an orphan with nothing to his name. Perhaps he could feel too inferior to pursue her because marrying her would ultimately mean becoming a leader in the Kirijo Group as well.