Yes, I had seen that exchange before typing my response. The way the convo went was actually NOT fine for a few reasons:
1. You became desperate-looking when you tried to get in on her break time. Yes, it sounded like she was telling you about the break as a way to convey she'd be free during that time (especially since she was telling it to you via texting), but it wasn't. And even if it was, you don't ever set up dates where she's implied there's a time limit 'cause she'll be on the date checking the time the entire time waiting for the deadline to come.
2. You asked her what I call the "question of dating death": "When does it suit you?" (which is a variation of "What days do you have free?") You're the MAN - you're supposed to be the one coming up with the activities and offering specific days that YOU are available. Instead, you left it up to her with your "let me know when it suits you and I'll see if I can make it too." I won't go into the whole "too many options = no options" theory, but suffice to say she doesn't want to have to THINK about WHEN she'll be available - she wants YOU to have an activity already thought out (including location and day/time) so she can just say "yes" and show up.
As for what you should do at this point? For one, she didn't send a counter-offer, so it's not looking promising. Still... here's what you do: assuming she'll contact you if you don't contact her, the next time she sends you a message, wait 2 hours and then
CALL HER up. Before this, though, already have in mind a place you can take her for an actual date (be it a coffee shop, comedy show, movie, etc.). When you call her up, do some light catching up (no more than a minute and a half), then say:
YOU: "Hey, I know you said you're busy til Sunday... let's do (x-activity) on Sunday or Tuesday night, which ever works best for you."
Then shut up and wait for her to answer. Seriously - once you've said this sentence, stop talking. If she starts going, "Um, mmm, well, er..." don't say ANYTHING until she gives you an answer. No jumping in and trying to interrupt the awkwardness - let her feel uncomfortable, but let her verbalize a definitive answer for you. She'll either say "Sure," "Let me think about it," or "I'm busy." If she says anything other than something similar to the first answer, she's not interested.
And if she doesn't contact you? Hit her up next week with a PHONE CALL and go through the same steps. And for the love of GOD, stop having random text convos with this chick - I'm totally against texting, but if you're going to do it you should only use it to get dates or a meet-up - no more of this "trying to build rapport through text" crap - it doesn't work, and it KILLS relationships. Hope this helps!