Adobe reader stopped working on iOS 13.4.1 iPad Pro

Your documents are not lost. Or better said, they shouldn't be lost.

You should still be able to access all of your document online using the document cloud via web browser.

You can download and backup those document from there.

You may also want to check if your device is synchronizing files properly, and more importantly, to check which other computer devices are currently sharing these files with your iOS device.

Now, if you acquired this app via the Apple store you need to seek support from the vendor, and follow their recommended guidance  how to troubleshoot the installtion and reinstalltion in your iOS mobile device.

However, uninstalling and reinstalling is not sufficient.

According to Apple guidance, after you ininstall  any app that was acquired from their app store, you have to go back to the store, sign in with your AppleID and check if the Reader Mobile App continues  to appear associated with your mobile device.

If it is,  remove or deactivate completely.

Then back on your device, perform a long press on the app icon and see if you can clear the application's cache.

After you clear the cache uninstall the app and  reboot the mobile device.

 Go back online to the Apple store and download  and install the app again.

See if this helps.