Wa `alaykum as-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
If the Quran slips unintentionally from your hands onto the floor, you have to pick it up instantly, remove whatever dust may have attached to it, resume your reading, or put the Quran in its normal place.
In his response to your question, Sheikh Muhammad Salih Al-Munajjid a prominent Saudi Muslim lecturer and author, states:
The Quran is the Word of Allah. It is the most Sacred Book. Muslims must respect and honor this Book. Our outward postures reflect our inner feelings of love, devotion, reverence, and submission to the Words of our Lord.
No Muslim doubts that it is obligatory to respect the Book of Allah, and the scholars are agreed that the one who deliberately mishandles it is a kafir (unbeliever).
At the same time, Allah says that there is no sin on one who is ignorant, forgetful, or who makes a mistake.
Allah describes the believers as saying what means: “Our Lord! Punish us not if we forget or fall into error” (Al-Baqarah 2:286)
Whoever has no free will in a matter, such as one who is forced to do something or who is asleep, is not sinning if he says or does something that goes against Islam.
You have not done anything that goes against Islam. When the Quran fell, it was not by any deliberate action on your part, so you have not fallen short in respecting it.
Although Islam tells us that we must repent from our sins and give them up, at the same time it warns us against falling prey to waswas (insinuating whispers of Satan) and despairing of the forgiveness and mercy of Allah.
Based on the above, if the Quran slips unintentionally from your hands onto the floor, you have to pick it up instantly, remove whatever dust may have attached to it, resume your reading, or put the Quran in its normal place.
Also, you should be sure that Allah will accept your repentance and grant you forgiveness as long as you repent sincerely. As stated in the fatwa, you have not done anything that goes against Islam. Therefore, there is no need for all that worry.
Allah Almighty knows best.