Have you tried not just
shutting down Mail but
actually deleting it so you can then
re-install it?
Side note: Make sure you know and can access your email settings (password, registration name, etc.)
before deleting the Mail app. That info should remain on the iPad, but never trust anything on a computer to be there when you need it! Better safe than sorry.
To
delete an app from your iOS device, even a built-in app:
'Hard' press and hold any app icon. You should get pop-up menu with "Edit Home Screen".
Tap "Edit Home Screen".
All apps should now have a little "x" on the upper, left-hand corner of their icon.
Tap the little "x" icon in the the Mail icon.
OR 'lightly touch' an app's icon and keep your finger on it. You should get a pop-up menu with either
a "Delete App" or the same "Edit Home Screen" menu.
Tap either "Edit Home Screen" (or "Delete App" if it is the Mail icon).
All apps should now have a little "x" on the upper, left-hand corner of their icon.
Tap the little "x" icon in the the Mail icon.
Open the App Store, search for "Mail" and re-install it.