Great advice in this thread. Powerlifter is right--she didn't flake, she just had to take care of her sick kid!
A girl that flakes DISAPPEARS. They don't return texts or calls at all. It makes sense; this allows them to drop a guy without an awkward conversation, yet STILL maintain a "good girl" image (calling out a girl on flaking is something of a social transgression).
Your girl didn't flake; however, as more time elapses between meets, her interest in you is going to drop. If you still want to pursue her, you are going to have to be the one to initiate it, because for her to ask you out after so long would be characteristic of someone that is desperate. Women very naturally have WAY better social skills than guys, so a woman that OVERTLY chases you is usually one that's a little "off."
Instead, look for her to "appear" a la Jophil- realize that something as subtle as bumping into her at a place you frequent is a woman's way of asking you out, similar to when a woman tells you about a place she really wants to go. The correct thing to do is RECOGNIZE her intent (not verbally, though!), and then ask her out--thus making her feel like a woman.
If you want to avoid FLAKING, that just requires a lot of rapport. Texting is the best flake prevention, because it keeps the lines of communication open. Even better, it can re-open lines of communication that haven't been used in a while--you can text a girl you had one date with a year ago and odds are you'll still get a response (if you didn't creep her out). Save phone calls for when the iron is "hot"-- i.e. when you know she has enough interest to pick up.