Can't access mail. Reverts to home screen

You might have a problematic email that is causing this issue and removing it on the server would help, if that is the reason why this is happening. I would first try completely closing the mail app and reset the iPad. That might fix it. No data is lost, so it's worth a try.

Press the Home button two times quickly. You'll see small previews of your recently used apps. Swipe left to find the app you want to close. Swipe up on the app's preview to close it.

To reset the device, press and hold both the Sleep/Wake and Home buttons for at least 10 seconds, until you see the Apple logo.

Actually, the would be the next suggestion that I would make. You won't lose any emails, you are simply deleting the account form the iPad. Give it a try. Just keep in mind that if that doesn't work, you might need to do some additional investigation on the server - meaning going into your email account on a web browser no see if you have an email with a really large attachment or a corrupt email that is causing problems.

In the meantime, delete the account, add it back and see how it goes. Good luck!

If you have synced your contacts and calendar from you email account then yes you will loose your contacts and calendar.

Just verify this by going into contacts and see where they sync from in the menu. It will show you email there them just deselect it and see if your contacts are still there or if most are missing.

Just take note if you put the email back on the device it will sync it again.

Good luck