In my opinion based on the Qur'an, if there is a third divorce where the man can marry someone else straight away, and the woman has to wait out her iddat period, there can be no reconciliation.
You may question the wisdom of the Qur'an behind not allowing a couple to re-marry after three genuine divorces, not heated 'talaq' pronouncements, but if they cannot get on after three attempts at marriage and two divorces, then the Qur'an is placing a huge 'get it right now or else' hurdle in the way.
After the third divorce the woman can stay single or genuinely marry another man, it is not a one-night-stand.
If this breaks down then Allah has put His proverbial hands up in the air in exasperation and allowed the original couple to re-marry if they are available.
As always, this is my understanding of the Qur'an and if I have missed something in its explanation of the divorce and marriage saga then I am open to correction, but it has to be Qur'anic based not 'scholarly' opinion.