Hi @Craig Tompkins ,
As AshokM-8240 has replied above, I wan to confirm what are specific error messages showing in event logs? And based on your description, these health mailboxes account don't exist, please check these accounts in ADUC and powershell again.
- Check health mailboxes in ADUC: Open up Active Directory Users and Computers(ADUC) and open up the group Microsoft Exchange System Objects. You will see a subgroup called Monitoring Mailboxes.
- Check health mailboxes in powershell (Check the health mailboxes of all the Exchange servers in the organization): Get-Mailbox -Monitoring
If these accounts don't exist in both side, I suggest you to try to recreate health mailboxes and check if this issue continues. Here's an article on recreating Health mailboxes for your reference: Exchange 2013/2016 Monitoring Mailboxes
If an Answer is helpful, please click "Accept Answer" and upvote it.
Note: Please follow the steps in our documentation to enable e-mail notifications if you want to receive the related email notification for this thread.