Apple → Email Sync Problem

We use Office 365 for our work email. One of my users is having a problem with keeping emails in sync. Her iPhone and desk iMac are fine. Her MBP does not stay in sync. I've deleted and reinstalled the email account but the problem is still there. She's running Sierra both the iMac and MBP. I do see a message at the bottom of the mailbox column that shows "Downloading Messages Paused (On Battery)" but that shouldn't impact the syncing of current messages. I've also tried taking the account offline and back online, but the problem is still there. Any ideas?

»support.apple.com/en-us/HT205263

Yep, like I said, that only applies to old messages. What she's seeing is messages that she's read, replied to, deleted, etc., still showing in the Inbox on the laptop as Unread. On the iPhone or iMac, they show correctly.