The third message says "just circling back on this." There is no question mark that matters. They would have to reopen the first mail, remember which of seven items was theirs, and invent a reply. Most people archive the nudge. You have not followed up. You have pinged.
A follow-up is a new ask that happens to be about the same decision. If it cannot stand alone, it is not a follow-up. It is a receipt that you are still waiting.
The old thread is not in their head
Monday's reader does not have Friday's context. A cold follow-up is a colder read. "This" is a pronoun with no noun. The reply cannot mirror an ask that is not on the page.
Restate the closed options. Restate the rejected path in one line. Restate the date as a day, not "still hoping for a quick turnaround." Urgency that lies is how follow-ups become noise. If Wednesday was real, say Wednesday. If it slipped, say the new day and why.
If the first message had seven questions, the follow-up is your chance to keep one.
Nudges train people to wait you out
A circle-back every two days, with no added information, tells them the deadline was theatre. They will wait for the version that contains a real date or a real consequence. Write that version now.
If nothing bad happens when they miss the date, do not invent a fire. Say you will proceed with B on Friday if you have not heard. That is an ask with a default. It is harsher than "circling back" and much easier to answer — including with a no.
Delivery is not the follow-up
They may not have seen the first one. A scanner may have. Opening is not acknowledging. You can check what the send path recorded, and you still restate the question. "Did you get this?" is a different job from "I still need a pick between A and B by Thursday." Do not merge them into a passive-aggressive ping.
They may have no AI. They still get a page. Resend the briefing, or send a shorter one that is complete. Do not send a one-liner that only works if they still have the original.
What you approve this time
The note can be shorter. It should still be yours: "I know this is the third time. I need the pick to tell the vendor." That is a human sentence. "Following up on my previous email" is a template, and they already know.
Confirm it. If they answer, the loop closes. If they do not, you have a record of a real ask, not a stack of nudges. That record is what you take into a call, or into proceeding with the default you already named.