Is it normal to not say good night before falling asleep?

Mention that it bothers you. Also, try to be understanding. If she is tired, she might plan on taking a quick nap and then just ends up staying asleep.

Hey no, that is not cool, especially if you talked about it. If she doesn't acknowledge it later or tell you that she's sorry and that it doesn't mean anything bad when she doesn't call, she's sending you a message, loud and clear. Girls will do this, they are emotionally smarter than you and you just have to be honest with them. It might be good if you say something, it might be good, because she might be testing how much you care, ans might e hoping that you acknowledge it. It may seem like your emotionally weak or uncaring if you don't. It's more likely shell feel that way so it's worth it to risk seeming insecure and possessive, because even a little of that is strengthening in a relationship.

Good night are words that I'm Ill-at ease if I don't share or hear from my special one

Yes, I had a long distance relationship, and sometimes ppl(in this case me) are too tired and fall asleep without noticing. But consider it like that and you'll be ok. She considered it that way. So if it worked 4 my x gf it can work 4 u