I met this girl few months ago. Recently, I felt she hasn't been responding to some of my text messages. And somehow I felt she didn't talk to me as much as before. Is it wrong if I wrote to her, asking if I have done anything to annoy or upset her, and apologize for specific instances in which I might have?
Do you ever see her in person? If so, do you get the impression something is wrong then too?
Typically I would suggest not basing things like that on text messages. Don't allow something like that to make you paranoid. Some people text all the time, some not so much. I've even known some people who are so damn confusing because they actually fall into both categories. They may text you all the time, then suddenly drop off and if you try talking to them, you are lucky to get one or two responses before they disappear. That may just be her way.
So, I guess I would say if it is JUST based on text messaging, try as much as you can just to let it slide.
Though, bottom line, no, I do not think it is wrong to ask a girl, or anybody really, if you have done something to upset them. As long as it isn't something you do constantly (otherwise people will think they have to walk on eggshells around you for fear that you'll think they are upset with you) if you are legitimately concerned that things are not okay between you and a friend/girlfriend/whatever, there is no harm in asking.
If they are a good person, then they'll talk to you about it either way. If there IS something wrong, then a good person would give you the opportunity to talk about it. If there truly is NOTHING wrong, then a good person would question why you thought something was, and that could lead you to explain and hopefully they can put you at ease as to why they seem to have drifted.
So, I guess the moral of the story is "pick your battles," so to speak. If you think you may just be over-reacting, or worried over nothing, then maybe don't say anything. Otherwise, if you are legitimately concerned, then you won't know if everything is okay unless you ask.
Good luck, friend. I hope everything turns out well.