If a girl I dated once replies when I invite her on a second date "I don't know if I can now because" and doesn't write later, did she turn me down?

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Assume rejection if a date doesn’t happen that’s not for sure another reason. Just say something like, “ok, I understand, let me know if you change your mind,” and stop contacting her. Keep your tone neutral and try not to sound like you’re blaming her for anything.

If she starts contacting you after that, then it’s because she wants to, and not because you’re pushing her to. You can assume she’s at least interested. Keep it light but interesting, and she might throw a few more indicators of interest your way. Then you can try to ask her out again.