How final is best and final?

If an Estate Agent says they’re taking best and final offers, you put yours in and it gets rejected, is that the end of the story?

What trumps what in terms of Estate Agents having to present offers to the vendor and Estate Agents saying it’s best and final? Is it just really poor form to offer a second time if you’ve already offered and been rejected in these circumstances? Or would a vendor not take you seriously / would they read into the fact you’ve ‘reneged’ on the best and final?

Thanks!

ETA - in England