The last email in the sequence is often the one that works
The short answer
The break-up email closes the loop politely and says you will stop. It reliably pulls replies because people respond to a door closing. Write it without blame, leave the door open, and mean it when you say you will stop.
The email you least expect to work is frequently the one that produces the answer.

Why it works
Nothing in the sequence creates urgency the way an ending does. A prospect who has been meaning to reply for two weeks suddenly has a reason to do it now.
It also removes pressure, which is exactly why it gets answered. You are not asking for anything, so replying costs nothing.
What to write
Short, and free of resentment:
- Say you are closing the loop, plainly.
- Leave the door open, in case the timing was simply wrong.
- No guilt, no "I have reached out five times".
The mistake that ruins it
Passive aggression. "Since I have not heard back despite several attempts" makes the reader the villain in your story, and people do not reply to that, they delete it. The tone should be relaxed, as though it genuinely does not matter much.
Mean it
If you say you will stop, stop. Continuing after a break-up email destroys the credibility of every message you sent before it, and it is precisely the behaviour that gets senders marked as spam.
It also matters for contact hygiene, which in Europe is not only good manners.
What the replies mean
Most fall into three buckets: genuinely not relevant, relevant but not now, or relevant and they simply forgot. The middle group is the valuable one, and it is worth recording a date to revisit them rather than treating it as a loss.
Frequently asked
What is a break-up email?
How do you write a break-up email?
Should I really stop after sending it?
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