First cold email - No response

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.