Dear questioner, thank you very much for your very important question.

On the authority of Ibn `Abbas (may Allah be pleased with him), that the Messenger of Allah (peace and blessings of Allah be upon him) said: “Verily Allah has pardoned my nation for their mistakes, their forgetfulness, and that which they have been forced to do under duress.” (Ibn Majah)

The Islamic Shari`ah has been lenient with the cases of forgetfulness, in consideration of the human conditions and reality. Every one of us is liable to erring and forgetfulness. With regard to fasting, Sheikh `Abdullah ibn Baz said in his fatwas compiled in a book entitled “Majmu` Al-Fatawa), “(Eating and drinking during fasting out of forgetfulness does not matter and one’s fast is valid, because Allah says at the end of surat Al-Baqarah:

“Our Lord! Punish us not if we forget or fall into error” (Al-Baqarah 2:286)

It was narrated from Abu Hurairah (may Allah be pleased with him) that the Prophet (peace be upon him) said: “Whoever forgets that he is fasting and eats or drinks, let him complete his fast, for the One Who fed him and gave him to drink was Allah.” (Al-Bukhari and Muslim)

The same applies even if he has intercourse because of forgetfulness; his fast is still valid according to the more correct of the two scholarly opinions, because of this verse and this hadith, and because the Prophet (peace be upon him) said: “Whoever breaks his fast in Ramadan out of forgetfulness, he does not have to make that day up and he does not have to offer any expiation (kafarah).” (Al-Hakim) This wording includes intercourse and other things that break the fast, if the fasting person does them because of forgetfulness. This is from the mercy, bounty and kindness of Allah, for which we praise and thank Him.                                                            

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Source: Taken with modifications from Islamqa.info