The breakup works because it removes pressure. After four touches, the reader knows what you sell; what they have not done is decide. A two-line email that says "I will stop here; if the timing is ever right, you know where I am" gives them a low-cost way to answer, and a surprising number do.
It also cleans the list: a "not now" is a signal to come back in six months, a "wrong person" is a referral, and silence after a breakup is a real no.