How can I resolve iPad Air backup issues?

If your iPad is not operating as expected, begin with a forced-restart of your iPad - as this will often clear an isolated software issue:

Force restart iPad (models with Face ID or with Touch ID in the top button)

If your iPad doesn’t have the Home button, do the following:

1. Press and quickly release the volume button nearest to the top button.
2. Press and quickly release the volume button farthest from the top button.
3. Press and hold the top button.
4. When the Apple logo appears, release the top button.

This support page outlines the natively supported backup methods for iPad and iPhone:

How to back up your iPhone, iPad, and iPod touch - Apple Support

Native iOS/iPadOS backup and restore processes are dependent upon iCloud, or connection to either Windows PC (with iTunes for Windows installed) or a Mac (with iTunes or Finder - as appropriate for the installed version of macOS).

Natively supported methods offer full system backup - consisting of data and device settings.

How to back up your iPhone, iPad, and iPod touch - Apple Support

You might be best advised to seek assistance directly from Apple Support. You can contact the Support Team using the Support link at top-right or bottom-left of this page.

Alternatively, you can initiate and manage your support cases from Apple devices using the excellent Apple Support App. If not already installed, the App can be downloaded from the App Store:

https://apps.apple.com/app/apple-support/id1130498044

You might also visit the Genius Bar at your local Apple Store or Apple Authorised Service Provider (AASP) - where the technicians will be able to assist with troubleshooting:

Genius Bar Reservation and Apple Support Options - Apple