Had this happen to me a few times, one time recently as well: texted a girl to set up a date and she doesn't reply for ages. In this case it was the next day, 24 hours later. To me, that shows a deep lack of interest, so I didn't reply and ignored her from then on.

What kind of limit do you have for yourself? Of course it should be said that, for me, if she apologizes for replying late and gives a reason, then it's fine and I carry on.