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Well you could try this.

1. Back up the phone

2. Delete all the email accounts on the phone and see if that fixes it. If it does you can add them back on. If not, back the phone up again after deleting, give the back up a different name

3. Restore the phone to factory settings through iTunes, test it, then restore from back up 1. If that recreates the problem again, repeat this step but use the other back up.
 
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