After 15 years in head hunting my gut instinct says "never". Here is an article by two executives from the US Headhunter Heidrick & Struggles which stumbles towards the same conclusion.
Why is it "never".
Once you hand in your notice the trust is gone. Trust is like glass.
If the present company really wanted to put something better on the table for you then they would have done it by now.
The best advice is to think long and hard. Make sure your decision to leaver is for the right reasons. Stick to it.
You finally decide to start looking for a new job. You go through a lengthy search process, you’re presented with an enticing career opportunity, and get an offer you’re fully prepared to accept. But when you tell your current employer you’re planning to leave, they surprise you with a counteroffer. And you’re left with a question you thought you had already answered: Should you stay or should you go?