Hello, yjchen0228,
Thanks for using Apple Support Communities, it's great to have you here. We want to help make sure that you are able to utilize the battery saving features of your iPad Air and have it auto-lock when expected.
The steps you've tried so far are great, we would have recommended them as well. We want to note that auto-lock may not kick in during certain use conditions; for example if you are using an app that streams video or a game. Certain apps can override the auto-lock feature so we would recommend testing it while your iPad is on the Home Screen, so that you can tell for sure that a specific app isn't causing the issue to occur. We would also recommend that you disconnect any Bluetooth devices that you may be using, to again isolate the potential for any interference that may be keeping the screen unlocked.
If the issue continues to occur while on the Home Screen and without any Bluetooth devices connected, we would recommend that you contact Apple directly. If support is available in your area, this will let you work directly with an advisor who can get some more information and see if any further troubleshooting may be available. You can start by reaching out here: Contact Apple Support
We hope that this information is helpful.
Have a great day!