A: Well, well well... Looks like we have a pretty narcissistic betta here ;). The young lad likes admiring himself, he? Gets depressed when you confiscate his alter ego? I can't really blame him. I get depressed when I don't have access to a mirror, too. Then again, I get even more depressed when I do have access to one LOL !!! (Especially in the morning). (but let's not go there for now)

So you need to rename your betta: "Romeo AND Juliet" (he can be both at the same time hehehehehe).

Is it OK to leave the mirror for him 24/7? I don't see why not. As I said, I allow my bettas to see each other 24/7 and they seem to be just fine ;). Sometimes, I switch their neighbors on them, to add a little spice to their otherwise pretty dull lives... If you do leave the mirror all the time, Mr. Betta will eventually somewhat lose interest in it, and only flare and check himself out occasionally. So if you are worried that he might exhaust himself flaring all day in front of the mirror, don't be. 

Another advantage to this arrangement: Your male will always have a nice close shave and perfect hair do hehehehehehe.

So go ahead you have Mama Faith's blessings.