I'm not a historian or anything, but I'll answer this question as best I can. Note that I'm Armenian, so take everything I say with a grain of salt if you want.

After the Nagorno-Karabagh Republic (NKR) declared independence in 1991, one of two things could have happened: one, other countries recognize it's independence and the NKR would be considered as a "real" country; two, no, or few, countries recognize it as a "real" country and so it technically remains a part of Azerbaijan.

The latter is what happened as no UN members recognizes the NKR as a State (including Armenia), hence, technically, the NKR is still a part of Azerbaijan. Obviously, since Azerbaijan doesn't actually control the territory and because the NKR has it's own government, constitution, laws, and military, not to mention missions in foreign countries (Washington D.C. (USA), Yerevan (Armenia), Potsdam (Germany), Moscow (Russia), Paris (France), New Delhi (India), Beirut (Lebanon), and Sydney (Australia)), it is considered as a de facto State.

As for the specific question of why it's not a part of Armenia is that since the peace talks of the NK war are still ongoing, Armenia doesn't want to take an action that could undo the work that's been, and still is being, done.