Very interesting case, I've been through something similar, only it was me who was unavailable due to business traveling, not the girl... Here's what I learned... whenever you go out on a date, you pump the attraction to a high level, from which it goes slowly down over the next few days, up to a week. If you meet again the next day or the day after tomorrow, you resume from a high attraction level and go higher up the ladder... This way you can close easily in 2-3 dates even with a "square" chick... By leaving two weeks between dates, you are resuming from an attraction level similar to the one before the previous date, not after the date... Does this make any sense?
About the invite to spend a night away, it gave her time to rationalize what was going to happen, and most likely was a bad move

Had you suggested while on a night out "Let's drive to South Beach for the night, we'll watch the sunrise there" and gotten a hotel room, that would probably have worked a lot better...
About how to proceed, your chances are reduced by the gaps between dates... and her answering you with such delays shows that you may have given her too much attention and she feels she can treat you anyway and that you will still be interested in her... If you can plow for a few dates only a couple of days apart, you may crack her code... otherwise, just leave her be... That's my take, anyway... Let me know how this ends... Bye!