Everybody agrees that following up matters and nobody wants to be the company that will not take silence for an answer. The usual way out of that tension is to pick a number — three touches, five touches — and treat it as a rule. It is the wrong variable.
It is not the count
People do not get annoyed because a company contacted them four times. They get annoyed because four contacts arrived that said nothing new, asked nothing answerable, and made it obvious that the sequence would have run identically whether they existed or not.
The same four messages, each with a different reason to exist, barely register as persistence. The count is not what people are reacting to.
Spacing is doing real work
A follow-up a day after the first contact reads as keen. A week later reads as diligent. Three weeks later reads as a new conversation. The interval sets the tone before a word is read, which makes it worth choosing on purpose rather than inheriting from whatever the tool suggested.
A pattern that tends to hold up: short gap for the first follow-up, while the original message is still plausibly in view. Longer gaps after that, widening each time. The sequence should feel like it is winding down, not winding up.
Change something each time
Every contact after the first should carry a reason that did not exist before. Something genuinely new is best — a relevant change, an answer to a question they raised, a piece of work that bears on their situation. Failing that, change the shape: a different channel, a shorter message, a different person, a question that can be answered in three words.
What does not work is the same message with escalating punctuation.
Decide in advance how it ends
The part most sequences lack is a defined stop. Without one, follow-up either runs forever at low intensity or stops arbitrarily when somebody loses interest in the spreadsheet.
Deciding the end at the start solves both. It also makes the last message much easier to write, because a plain, friendly close — telling someone you will stop here and leaving the door open — is a genuinely good message to receive. It quite often gets a reply when nothing else did, precisely because it asks for nothing.
The standard
A simple one: would you be comfortable if this person saw the entire sequence laid out at once, in order, with the gaps? If the honest answer is yes, the cadence is fine, whatever the number. If it is no, adding a longer delay will not fix it — the messages are the problem.