How to respond to someone who keeps flaking?

A single flake usually means nothing. People have bad weeks, double-book, or lose track of a text. What you are looking at is the sequence. If the plan has moved twice already, the new cancellation tells you the first two weren't accidents, and the apology that comes with it is doing the job of keeping you interested without costing her anything. Look at how she handles the reschedule. Does she pick a day, or does she say 'let's do something soon'? Does she bring up the plan herself, or wait for you? Someone who wants to see you will usually be specific and will propose the next step. Someone who is lukewarm will apologize warmly and leave the date open. The warmth of the apology is not evidence of interest. The concrete offer is.

Also notice what she does with your replies. If you have been flexible and she still hasn't landed on a time, the problem is not your scheduling. Her side of the calendar is the thing that isn't moving. That is the thing you are reading, and it changes how much effort the next message deserves.

Replies that work here share a shape: they acknowledge the cancellation in a sentence, then make one concrete offer with a day and a rough time. The offer should be easy to say yes to and easy to decline. A message that proposes a specific evening at a specific kind of place gives her something to accept or refuse. A message that asks what works for her makes her do the planning, which is the labour she has been avoiding.

The acknowledgement should be light and free of accusation. A short line that the plan fell through is enough. Leave out any comment about how often it has happened, any question about whether she is still into it, and any joke that hints at the pattern. Those lines turn a scheduling issue into a conversation about her character, and she will answer that conversation instead of the offer. The draft should read as a normal plan that happens to be easy to make, with no subtext you have to defend later.

Give her a day or two after a cancellation before you propose anything new. Replying within the hour makes you look available for anything, and it tells her the cancellation cost her nothing. Once you have sent a concrete offer, wait a full day or two for an answer. If she confirms, plan the details and let it be. If she replies with another vague 'soon' or doesn't reply, send one short follow-up at most, a few days later, that restates the offer in case it got buried. Do not send a second apology-seeking message, and do not check whether she read it.

If the third concrete offer also gets no commitment, stop proposing. You don't need to say anything dramatic. Stop initiating and see whether she does. If she never picks the thread back up, you have your answer, and the cost of finding it out was a few texts rather than months of waiting around. If she comes back with a specific plan, that counts, and you can decide whether one good follow-through is enough to keep going.