Force quit the Mail app: Forcing the Mail app from running in the background will close all app functions. Then, tap on the Mail app icon to reopen the app. This should refresh app functions and fix any issues caused by temporary app glitches.
Update iOS software: All Apple apps are part of iOS software, and the company adds new features and bug fixes via iOS updates only. Mail stuck on checking for new messages might be due to a bug. So, install any new software updates to fix it accordingly.
Reinstall the Mail app: Custom app settings can also display such errors. If you can’t identify them, uninstall the Mail app and reinstall a fresh app copy. Then, set up the Mail app again and see if this fixes the issue.