Cold after third date

I had tree dates with this woman. Everything went just perfect (I had first dates with others and after most of them I didn’t had a good feeling and also didn’t get second dates).
During this third date we spoke about a fourth activity two days later. I contacted her that day but we couldn't meet anymore (I contacted her too late, my fault!). Then there was no reaction anymore on another message from me two days later (but this was on her work e-mail).

I'm doubting now to contact her again to meet this weekend.

But I read two different possibilities now:
Should the man always take the initiative for the next date?
OR
Is she supposed now to contact me again (because she hasn’t replied (yet) on my previous message)?

J

In my mind, if you want to see someone again, you should ask and not wait for them to initiate. Maybe she was busy at work and missed your email. Try reaching out to her again, if she declines or doesn't reply, then it's probably best to move on.

Well, I first contacted her by text message. No reaction. Then I got a reply on my mail.

"Hi, you do not neet to apologize for anything. I am not angry or upset at all. Things like he one on Monday just happen sometimes. Anyone can have a bad day. I do not want to hurt you. You are a nice guy. But it is true that I do not feel the same as you probably do and I do not want our friendship to progress in any other thing than friendship. I do not want to be the bad side of the story neither but to be honest, I am not in the same mood as you are. I prefer to give us some time to think about it and to let you time to keep distance from me. If after this time you want to keep me as a friend I will be there. I hope you understand."

So, she rejects me, but this messages gives space of doubt.
Time to think about it... etc?
What does she expect? That I contact her again in two months or so?

It's difficult for me to put this reply in the right frame, because it's contrasting to the way we behaved (kissing and holding hands).

I hate to say it but She definitely isn't interested in any romantic relationship with you. I don't think she expects you to contact her at all and is hoping you will forget. I wouldn't tell any man that I'm interested in to contact me in a couple of months, no matter how busy she is, if she's interested in more than friends she would make time.

She's just trying to be nice. She's made it clear she isn't into you as more than a friend but she wanted to try and let you down easy. It's best if you move on and find someone else to date.