How many follow-ups are you all sending before calling a prospect cold?

We noticed 70% of our replies come from the 2nd or 3rd message, but sending "Just bumping this to the top of your inbox" was getting us blocked.

We switched to sending a 30-second quick visual breakdown or a relevant free asset instead of a reminder. Replies went up without burning the relationship.

What’s your go-to non-annoying follow-up angle that actually gets a response?