What if the wife claims that he divorced her but he denies it or forgot it?

If the wife claims that the husband divorced her, and he denies it, then his word should be accepted, unless she brings proof that divorce took place. This is as far as judgments and rulings are concerned, but the matter rests with Allah Who can see what is in his heart. A judgement may be passed stating that a man can keep his wife, when in fact she is not permissible for him before Allah, if he did in fact divorce her and this was the third divorce (talaq). 

Ibn Qudaamah (may Allah have mercy on him) said in al-Mughni (7/387): If a woman claims that her husband divorced her and he denies it, then his word should be accepted, because the basic principle is that the marriage remains in effect and there is no divorce, unless she has proof of what she claimed, and her proof will not be accepted unless it is supported by two witnesses of sound character. 

If there is no proof, should he be asked to swear an oath? There are two reports concerning that. Abu’l-Khattaab narrated that he should be asked to swear an oath, and this is the correct view, because the Prophet (peace and blessings of Allah be upon him) said: “But the oath is to be sworn by the one against whom the claim is made” and “The oath is to be sworn by the one who denied it.” 

If he divorced her three times and she heard it, but he denied it and she has proof from two witnesses of sound character, then it is not permissible for her to let him be intimate with her, and she has to avoid him as much as she can, and refuse to let him be intimate if he wants that, and she should give up something to make him let her go if she can. Ahmad said: She cannot stay with him. He also said: She should give up something to make him let her go if she can, but if she is forced to stay with him, she should not adorn herself for him or come near him, and she should avoid him as much as she can. If two witnesses of good character testify to that then she should not stay with him. This is the view of most of the scholars. End quote. 

Based on that, so long as you do not remember this divorce, then it cannot be counted against you; before the judge and before people, you have only divorced your wife once. 

But if your wife is certain that this divorce took place, then she should act on that basis, and if another divorce takes place, then before the judge this is a second divorce, but for your wife this is the third, so she has to give up something so that you will let her go if she can and it is haraam for her to stay with you, as stated above in the words of Imam Ahmad (may Allah have mercy on him). 

And Allah knows best.