My IPad Air often shutdowns now showing low battery but, battery is not low.

How are you able to be sure of the battery level - other than by using the battery status indicator in iPad settings or the icon at top-right of the screen? Just connecting the iPad to a Power Adapter is no guarantee of successful charging.

These support pages should help with troubleshooting battery and charging issues:

Charge and monitor the iPad battery - Apple Support

If your iPad won't charge – Apple Support

Troubleshooting generally requires substitution of the Power Adapter and cable for another known-good item. Most models of iPad require a Power Adapter rated at 12W or greater to reliably charge. 5W Power Adapters intended for older models of iPhone are inadequate to charge an iPad; if the iPad charges at all, charging will be very slow.

Be aware that many computer USB ports cannot source sufficient power to charge an iPad. Unless explicitly designed for charging connected devices, computer USB ports are typically limited to 0.5-1A @5V (i.e., 2.5-5.0W).

If you continue to experience difficulties when using an appropriate Power Adapter of 12W or greater, you might be best advised to seek assistance directly from from Apple Support - and request a remote diagnostic test. You can contact the Support Team using the Support link at top-right or bottom-left of this page. Alternatively and perhaps easier, you can initiate and manage your support cases using the excellent Apple Support App. If not already installed on your iPad, the App can be downloaded from the App Store:

https://apps.apple.com/gb/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 test and assess your iPad, Power Adapter and cable(s):

Genius Bar Reservation and Apple Support Options - Apple

Indeed your clarification of behaviour and the iPad model would suggest an aging/failing battery that has reaching the end of its useful lifespan. Unless you have previously had the battery replaced, the iPad2’s battery will be approximately 12 years old.

As the iPad2 is long-ago obsolete, hardware support has ended. Apple no longer offer a battery replacement service for your iPad. Unless you are able to find an independent repair shop with an available third-party battery, battery replacement is unlikely to be possible - or cost effective. Be aware that the iPad2 has a 32-bit system architecture; all compatible 32-bit Apps have been withdrawn from the Apple App Store and can no longer be re-installed.

You would be best advised to consider replacement with a much newer iPad. Of current models, even the entry-level iPad9 supports iPadOS16 - and will significantly outperform your iPad2 in every respect.