And he said to the one whom he knew would go free, "Mention me before your master." But Satan made him forget the mention [to] his master, and he [i.e., Joseph] remained in prison several years.
Yusuf asks the King's Distiller to mention Him to the King
Yusuf knew that the distiller would be saved. So discretely, so that the other man's suspicion that he would be crucified would not intensify, he said,
اذْكُرْنِى عِندَ رَبِّكَ
(Mention me to your King.) asking him to mention his story to the king. That man forgot Yusuf's request and did not mention his story to the king, a plot from the devil, so that Allah's Prophet would not leave the prison. This is the correct meaning of,
فَأَنْسَاهُ الشَّيْطَـنُ ذِكْرَ رَبِّهِ
(But Shaytan made him forget to mention it to his master.) that it refers to the man who was saved. As was said by Mujahid, Muhammad bin Ishaq and several others. As for, `a few years', or, Bida` in Arabic, it means between three and nine, according to Mujahid and Qatadah. Wahb bin Munabbih said, "Ayyub suffered from the illness for seven years, Yusuf remained in prison for seven years and Bukhtanassar (Nebuchadnezzar - Chaldean king of Babylon) was tormented for seven years."
Ma'arif al-Qur'an
Mufti Muhammad ShafiOn ayahs 42–43
After that, to the person about whom Sayyidna Yusuf (علیہ السلام) had gathered from the interpretation of his dream that he would be released, he said: When you are released from the prison, mention me before your master as the innocent person who is still languishing in the prison. But, once released, this person forgot about this message of Sayyidna Yusuf (علیہ السلام) ، as a result of which, his freedom was further delayed and he had to stay in prison for a few more years. The word used in the Qur’ an is: بِضْعَ سِنِينَ (bid'a sinin: a few years). This word holds good for a figure between three to nine. Some commentators have said that he had to live in the prison for a period of seven more years.
Tazkirul Quran
Maulana Wahiduddin KhanOn ayahs 42–44
Of the two youths who were put in jail, one was a bread maker and the other was a wine-server to the king of Egypt. Both were accused of trying to poison the food of the king. On investigation, the wine-server proved to be innocent of the allegation. He was released from the jail and was again appointed as a wine-server to the king. His dream meant that he was serving wine to the king in dream and after few days he would really serve wine while awake. The bread maker was proved guilty. He was hanged and left for the birds to peck at his body and, in this way, be a lesson to the people. Both the interpretations of Joseph proved to be correct but, after reaching the palace, the wine-server forgot to mention Joseph to the king as promised. He remembered his promise only when the king had a dream and asked his courtiers to interpret it.
Uthmani text of the Madinah mushaf (King Fahd Complex). Translation: Saheeh International. Tafsir via Quran.com.