Attunement is required to read it, but the benefits stay
The book requires attunement to open:
A heavy clasp, wrought to look like angel wings, keeps the book's contents secure. Only a creature of good alignment that is attuned to the book can release the clasp that holds it shut.
After that, it requires to be read for 80 hours by the attuned creature. That is, attunement is not sufficient a condition to gain the benefits of the book:
Once the book is opened, the attuned creature must spend 80 hours reading and
studying the book to digest its contents and gain its benefits.
After attuning to the book to open it, as well as qualifying as the only person who can currently read it, as well as spending the required 80 hours to finish reading it, you gain the benefits as listed.
And then, once the book is read and the benefits are gained, it vanishes:
As soon as the book is read, it vanishes to some other corner of the multiverse where its moral guidance can bring light to a darkened world.
One of the benefits you gain from this book is increased Wisdom:
Increased Wisdom. After you spend the requisite amount of time reading and studying the book, your Wisdom score increases by 2, to a maximum of 24. You can't gain this benefit from the book more than once.
Of particular interest is the note: [y]ou can't gain this benefit from the book more than once. This implies you can find the book again and gain the other benefits more than once. This means that those other benefits you gained on your first attunement must have remained with you the second time around; otherwise you cannot gain them more than once.
So we must conclude that the benefits stay with you after your attunement with the item breaks for the first time, due to finishing reading it.