Never expect anyone to reach out to you. You have to reach out to them over and over if you are interested.
If they see the value in what you are doing, they will reply or reach out to you, but never expect them to do so.
This applies to everyone, mentors, investors, customers.
You have to be proactive all the time.
Being proactive and contacting people over and over is fine for a while if you're "hustling" but eventually it just becomes spam, you sound desperate, and you'll be hurting rather than helping your chances.
Also, if you feel your proposition is good enough and you don't get the response you were after, then move on and focus on getting your pitch to the right people.
1-2 weeks later - Second cold email - No response
Monthly update/touch up - No response
Move on.
Some people would consider the second or third email as spam, that is fine. If they block you, that means that was a dead end anyway.
My experience is that people are busy and we forget to reply sometimes. 3 emails in a row, in a matter of days, would be spam for me too.