You're not supposed to actually fix it.
The point of the broken mirror is it adds a bit of depth to your character - he keeps breaking it because he can't stand to look at himself.
gaming.stackexchange.com/users/2578/BlueRaja - Danny Pflughoeft
Adam broke the mirror because looking in it reminds him of his augmentations, and looking at his augmentations reminds him of his failure to protect Megan.
He is not going to fix it.
It has absolutely nothing to do with Eidos Montreal deciding not to program in any reflective surfaces and the complexities therein.
;)
gaming.stackexchange.com/users/9300/CyberSkull
You cannot fix the mirror, it simply adds a story element to the game.
Screenshots of the emails for anyone interested: Email on Jensen's computer:
http://i.imgur.com/A1JuD.jpg
Email on lobby computer:
http://i.imgur.com/Fsk2Q.jpg Mirror with note: http://i.imgur.com/lerp9.jpg
gaming.stackexchange.com/users/20055/Lemmings19
Out of story reason: Showing a mirror in an FPS requires an extremely high quality of animation for the main character to avoid brekaing immersion; these are animations that normally would never be visible in first person.
As such, the dev cost of including a mirror is very high relative to rare occurrences.
This is why the mirror is not reflective, even though it's a mirror.
Not only that, the frequent broken and missing mirrors in the game call back to the orignal DX, which featured really terrible mirrors (unsynced images, bad animation).
By breaking all the mirrors they could avoid the same thing happening again
gaming.stackexchange.com/users/26042/Lawton
A far as I can tell from some research, there is no actual way to get the mirror fixed.
gaming.stackexchange.com/users/11502/Ash
I'm going crazy! This mirror has been broken for ages, I've e-mailed the landlord about it multiple times, but they keep telling me off.  However, when I took a quick sneak peak at their reception computer, they have an e-mail sitting in their inbox from the mirror supplier asking them to come pick it up since it's been waiting for over a month.  How do I get them to fix my mirror?
How do I fix my bathroom mirror
gaming.stackexchange.com
<deus-ex-human-revolution>
gaming.stackexchange.com/questions/51047
gaming.stackexchange.com/users/4815/Konerak
You're not supposed to fix it and there is not way in the game to get the mirror fixed. The broken mirror, beyond the fact that adds up to the narrative, is a common technique by developers to hide the extra costs required to program things that a mirror might reflect.
The community confirms that there is no way of fixing the mirror.