The short reasons is that it's because he doesn't want to become an officer and/or, because he feels that his skills are best served as an NCO.
Note that O'Brien has repeatedly shown a mild dislike of 'officer-types' in general.
O'BRIEN: With all due respect, I think you're riding the men a bit hard. You have to understand, they're out of their element.
They're not bridge officers, they haven't been to Starfleet Academy.
They're engineers. They're used to being given a problem to solve,
then going out and figuring out how to do it.
Added to that is that fact that Starfleet would apparently require him to attend the Academy for several years if he wanted to become an officer, as we can see from this exchange between (Enlisted medic) Simon Tarses and (Commissioned Officer) Captain Picard:
TARSES: Yes, sir. All my life I wanted to be in Starfleet. I went to the Academy's training programme for enlisted personnel. I took
training as a medical technician and I served at several outposts. The
day that I was posted to the Enterprise was the happiest day of my
PICARD: Did you ever consider applying to the Academy, going the whole route, apply to become an officer?
TARSES: My parents wanted me to. And then I thought about it. I used
to sit under this big tree near the parade grounds ... I used to sit
under that tree and watch the drills, picture myself an officer. I
know that it would have made my mother very happy, but.
PICARD: You didn't do it.
TARSES: No. I was eighteen, and eager. The last thing I wanted to do was spend four years sitting in classrooms. I wanted to be out
there, travelling the stars. I didn't want to wait for anything.
Even if he could get a field commission or earn credit for his long service, becoming an officer would simply take him away from what he seems to enjoy the most, working in engineering and and teaching others. On DS9 he's already a Department Head (and Chief of Operations with his own engineering teams) so gaining a commission really doesn't do much for him.