Alright, never let it be said I sit here and tell people what to do; only in extreme cases. Yo're all big boys and have your own adventures to enjoy.
However, I will conclude (my own points) here. Let's imagine we are both in the situation of the OP. At this stage (immediately after the flake):
1) Your tack is to counter-offer. Fine, I see a vague, though unreasoned logic in that there is a small chance that she 'may' in fact be interested, her excuse 'may' have been legit and she 'may' turn up second time round, you 'might' get laid, and you 'might' live happily ever after. Or any combination thereof.
However, I will back-pedal slightly here and say that you are not even rationalising, because that would imply some logical thought of reasoning. What you are in fact doing is hypothesising, or even living in blind hope. Currently, you have no evidence other than a casual 'Some other time?' to suggest she's worth wasting any more time waiting for, for whatever you want. Because that is what you are currently doing: waiting, and hoping, and that's what you will continue doing until she does it a second time, having wasted another evening of your time, waiting and hoping. Your SECOND offer tells her that as well. If all she gets out of that is an ego boost, she's still got more than you; you who is now at a detriment, because she wasted two evenings of your life that you kept aside.
2) My own tack is not to ignore and go NC, (as you see, some more cutthroat members see this as highly disrespectful; and I am inclined to agree, but am less conservative than they). I might even go as far as to send a word of condolence for her work stresses. But I will not be waiting around and I will be forcing her hand one way or another, by putting the ball in her court - 'Let me know when you're less busy'. I will be doing this for the following reasons; not hopes, not 'mights' or 'what ifs', or my own emotive projection-transference hypotheses, but for these REASONS that she has shown me:
a) The flake. In short, she's wasted my time and shows no remorse.
b) Half of her excuse may be 'legit', but the other half is rude - she 'forgot'. That being, she holds me an my time in such low regard already that she 'forgot'. Words my friend, listen to and read the words. A woman will tell you half the truth, in order to avoid 'hurting your feelings'. To her message, I read, 'I can't be @rsed and I don't even give a sh!t that I wasted your time'.
c) No (conclusive) counter offer; rather a cursory 'shall we, shalln't we bother?' kind of half @rsed counter.
d) She's a lawyer. This won't be the last time it happens.
Ask yourself this; how much is your time worth? Think like a lawyer or a business man, if a client flaked, saying they 'forgot'... meh, doesn't fill me with inspiration about the intentions of this person/company. For some people, it really is that back and white. One strike and out.