iPad Pro iPadOS 14.5, last highlights and notes on Books is lost every time I close Books or shut down
iOS and iPadOS 14.5 are currently beta operating systems and are expected to have bugs and other random issues. As of this writing, they are on developer beta 2 and public beta 1. There will likely be over 5 betas before this version is officially released.
You should not use beta software on your primary devices or on any devices on which you depend. You should report any bugs you find to Apple using the Feedback app (purple/pink icon) that appears on your Home Screen or app drawer when you install beta software on your Apple devices. If you are not willing to live with bugs/issues and report them to Apple, you should not install beta software.
There’s nothing anyone here can do to help you with beta Apple software. If you report the bugs to Apple, they will likely fix it before releasing the final version.
You can either downgrade your device to a final version of iPadOS such as 14.4 (recommended) or wait until the next beta is released and hope it is fixed by then, but there are no guarantees about beta software and the next version could actually be worse than the current one you have.
Reinstall Apple Books
Sometimes with beta software resetting settings, apps or even the whole device might work. You can try reinstalling Apple Books.

Make a backup of all of your files. PDFs, books and anything you have imported into Apple Books. You already have a backup if you use iCloud and Apple Books and iCloud Drive are enabled on Preferences &gt; Your Name &gt; iCloud. Make sure the backup has finished synchronization before proceeding.

Delete the Apple Books app and download it again from the App Store. Then try again and see if it fixes your issue.