Thanks for that info and choosing the Apple Support Communities. If I understand correctly, you are unable to mark reminders as complete in the Reminders app, as it un-checks itself on your iPhone. If you haven't already, please force close the Reminders app and restart your device as iOS clears cached data and does other system optimizations when you turn your device off and on.
Force an app to close on your iPhone, iPad, or iPod touch
Restart your iPhone, iPad, or iPod touch
If you're still having this issue, please remove the Reminders app and reinstall the app, as this removes configuration files that maybe causing this issue.
Remove a built-in app from your Home screen
- On your iOS device, touch and hold the app lightly until it jiggles. If the app doesn't jiggle, make sure that you're not pressing too hard.
- Tap on the app, then tap Remove.
- Press the Home button to finish.
If you have an Apple Watch, removing an app from your iPhone also removes that app from your Apple Watch.
Restore a built-in app that you removed
- On your iOS device, go to the App Store.
- Search for the app. Make sure that you use the exact name of the app. Find the correct name of built-in apps.
- Tap to restore the app.
- Wait for the app to restore, then open it from your Home screen.
If you have an Apple Watch, restoring an app to your iPhone also restores that app to your Apple Watch.