Hello GarlockPrinting!
Are the mail accounts from an Exchange profile? Was there a recent change to the device policy on your end or was the policy reapplied?
If so, have the end user enter their Exchange password and allow the device to synchronize.
Devices that are not configured to receive Exchange ActiveSync profiles will not experience this issue. Once the affected device completes mailbox synchronization, the issue should not appear again.
If you are still experiecing the issue, please provide more details on the type of mail account that is configured on the iOS device and if there were any recent changes made to the device policy.
Thank you for posting at the Community Portal! :)
Kindly,
Kequa