Maybe its just me. I seriously find it rude when you were conversing with someone and they can just stop replying your last message.

Fallen asleep?
Shouldn't you reply in the morning with an apology like "I'd fell asleep...... And didn't reply/hence the late reply....... Good morning by the way"
That's what they were being taught no? Where are their manners? You'll greet your family members/roomies/housemates/whoever you see in the morning right? Unless you are staying alone.

Busy at work till forgot to reply?
I don't mind if they reply after work, a day after (because too busy till forgot about it).

AT LEAST YOU'LL REPLY!

Or if you are going to sleep and can't continue the conversation, just say! Does it hurt or kill you to say that?

If you are watching a show, don't say its alright to continue the conversation, because its NOT ALRIGHT!