Below is a translation of a section from the book Tilawat al-Quran al-Majeed by Sheikh Abdullah Sirajuddin1. The footnotes are mine.
Al-Tirmidhi narrated the following narration, and said it was sound:
On the authority of Ibn Abbas (may Allah be pleased with him and his father) who said that the Messenger of Allah ﷺ said:
Indeed the one who has nothing of the Quran in his heart is like a ruined house.
Abu Dawud, al-Tirmidhi and others narrate from Anas (may Allah be pleased with him) that the Messenger of Allah ﷺ said:
The rewards of my Ummah were shown to me, even the (reward for) the speck of dirt which a man removes from the Masjid. And the sins of my Ummah were (also) shown to me. I did not see amongst them a sin greater than a Surah or Ayah of the Quran which were given to a man which he later forgot.
Abu Dawud narrates from S’ad ibn Ubadah (may Allah be pleased with him) that the Messenger of Allah ﷺ said:
There is no person who recites the Quran and then forgets it, except that he will meet Allah on the day of judgement ajzam.
The meaning of ajzam is a person afflicted with the illness of juzaam which is an illness in which parts of the flesh are cut off.
Most of the Ulema took the position that forgetting the Quran, whether all of it or a part of it, is regarded as a major sin (kabirah) as proven by the fierce warnings narrated in the Hadith. However, as mentioned by al-Jalal al-Bulqini, al-Zarkashi and others; it is only considered a major sin if it (the forgetting) was due to laziness or neglect (from considering it unimportant). If however a person forgot due to an illness, old age or something similar, then they are not counted under this ruling as mentioned in Sharh al-Adhkar.2
Al-Hafiz al-Suyuti said in al-Itqan: Forgetting the Quran is a major sin as clearly stated by al-Nawawi in al-Rawdah.
And the fierce warnings narrated in the aforementioned Hadiths were used as evidence for this.3
1] Page 36-37
2] In addition, some of our teachers have stated that as long as a person is trying to remember what he has forgotten, he will not be punished, inshallah.
3] It is also worth noting that many of the scholars did not interpret this Hadith to refer to a person who has forgotten Quran that he once memorised. Rather, they said it referred to someone who forgets how to recite the Quran (whilst looking at the text) after having once known how to recite it. Mulla Ali Qari states this to be the Hanafi position in Sharh Mishkat.