Every time I try to open my Mail app it flashes open but then closes right away.
When I go into Settings > Mail it says "ACCOUNTS ARE CURRENTLY SYNCING." -- but I don't show anywhere that it is syncing to my iPad.
Any suggestions??
iPhone 5s
First, reset the phone by holding the sleep and home button for about 10sec, until the Apple logo comes back again. You will not lose any data by resetting, but it can cure some glitches.
Restoring for the latest backup would be the next step after that:
How to erase your iOS device and then set it up as a new device or restore it from backups
If this does not work, delete the account and set it up again.
Mail app flashes open but closes immediately
