Ipad mini shutting down

The symptoms that you describe may indeed suggest a failing battery.

Are you able to use the iPad while remaining connected to your Power Adapter - without recurrence of shut-down or a crash? If yes, while monitoring the indicated battery state, disconnect the Power Adapter; if the indicated battery state suddenly falls, or the iPad shuts-off, this test demonstrates the iPad battery having reached the end of its usable life:

iPad Repair & Service - Apple Support

Otherwise, 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

Whether or not a device qualifies for trade-in will vary. If trading-in through Apple, you can assess eligibility - and possible value subject to acceptance - here:

Apple Trade In - Apple

You are very welcome.