Text messaging isn't like instant messaging. I actually don't quite get it when people feel the need to excuse themselves from a "conversation" via text - the whole makeup of text messaging is so that people can get back to the message on their own time, like e-mail. Unless it was an emergency or I take an unusual amount of time, I don't feel the need to apologize, and I don't expect anyone else to apologize to me. Don't sweat it too much - it's likely not her ignoring you. She may have forgotten it or just didn't feel like talking, or been busy.
There are many reasons. Don't feel bad, guy or girl a lot of people do this. I would apologize or say I had to go rather than leave someone hanging, but most people don't think of it that way. Usually what happens is the person gets busy and is either away from the phone / forgets the message. It doesn't mean you were boring or she doesn't like you. Good luck! I know how annoying that can be!
I stop replying to him for a number of reasons! Maybe I really don't like him and I can't put up with texting him anymore so I just stop. Or he's giving me one worded replies. I could've fallen asleep and if that happens, I'd apologize if I like the guy but if I don't like him, I'm not going to text him anything unless he texts me again. Or I could've gotten busy so suddenly that texting him back slips my mind. Another reason might be that I saw the text and couldn't think of a clever way to reply or something to say and though I had all the intentions of replying, I forgot to reply to it. But yeah, it can be annoying when a person doesn't text back so I hope this helped!
Mainly if the conversation has dwindled to a point of going nowhere. Also, sometimes I just get tired and fall asleep. Personally, I would never intentionally stop replying without some kind of end to the conversation, because I find that to be rude. Even if I happen to be mad or annoyed with the person I am texting. Hope this helps.