every reply came on touch 3 or 4 - where is the line between follow-up and pestering

Your distribution is normal, mine looks the same shape - roughly 15% of replies on the first message, 25% on the second, 35% on the third, the rest on the last one. Nobody replies to a stranger's first email unless the timing is lucky.

On where to stop, use the marginal number rather than a feeling. Touch four brought you two replies from 120 sends and one complaint. Touch five will bring less than that. When a touch produces under about 1% replies, it is buying you nothing and spending something.

One complaint in 120 is not automatically a targeting failure, but it is a signal worth reading - go and look at that specific contact and ask honestly whether they were ever a fit. If the answer is no, your list is the problem and no cadence fixes a list.

Housekeeping before you scale this past 120: send from a separate domain, not your main one. Get SPF, DKIM and DMARC aligned on that domain and check alignment with a real test rather than assuming your provider did it. Plain text, no tracking pixel, no images, no unsubscribe footer that makes a one-to-one email look like a newsletter, because that is what pushes a personal message into a promotions tab.

Daily volume is not your constraint at this size - a paid mailbox is good for a couple of thousand messages a day, a trial account far less - but that ceiling is irrelevant when you are sending forty. Complaints are the constraint. One person marking you as spam out of forty is a far worse signal than one out of two thousand.

Four touches is fine. Twelve days is too fast for a clinic - these people open email between patients and your whole sequence ran while one of them was on holiday.

I run four over about three weeks: day 0, day 4, day 11, day 21. Same rule as yours, every follow-up carries something new, never just bumping this to the top of your inbox. The last one is two lines and closes the loop cleanly: I will stop here, if this becomes relevant later reply to this email and I will pick it up. No guilt, no last chance, no fake deadline. Roughly a third of my eventual calls come from someone replying to that final message weeks later, and they reply to it precisely because it did not push.

Politely: 120 contacts and seven replies is not enough data to tune a cadence on. You are optimising the gap between messages when the two variables that matter are who is on the list and what the first line says.

The other thing nobody mentions at this size - your sending setup is doing more work than your copy. If those 120 went from the same domain your customers get invoices from, and a few of them marked it as spam, you have quietly damaged something that matters much more than this campaign.

Space them 4, 7, 10 days. Stop at four. One angry reply per hundred is the price of the channel, one per twenty is a list problem.

The change that moved my numbers was cutting touch one down to four lines with exactly one question in it. Mine used to have a paragraph about the product and a link to book a call, and it got nothing. Now it is: the specific thing I noticed on their site, one sentence on what I do about it, one question they can answer with a yes or a no, and my name. No link at all in the first email.

Replies went from about two per hundred to about six per hundred, and more of them were actual sentences rather than one word brush-offs.