The full error message might be similar to:
WARNING: The object contoso.com/Microsoft Exchange System Objects/Monitoring
Mailboxes/HealthMailboxd52c1cfaed1243c5b424f20726c21abb has been corrupted or isn't compatible with Microsoft support
requirements, and it's in an inconsistent state. The following validation errors happened:
WARNING: Database is mandatory on UserMailbox.
The solution here is quite simple according to the following Microsoft Technet Blog posting and includes the following steps:
1.) Stop the "Microsoft Exchange Health Manager Recovery" & "Microsoft Exchange Health Manager" on all your Exchange 2016 Server
2.) Disable existing health mailboxes via:
Get-Mailbox -Monitoring | Disable-Mailbox
3.) Open "Microsoft Exchange System Objects -> Monitoring Mailboxes" in your AD and delete all health mailbox user accounts as mentioned in the blog above.
4.) Wait for AD replication or force AD replication.
7) Start the "Microsoft Exchange Health Manager Recovery" on all Exchange Server 2016 servers (this will automatically start the "Microsoft Exchange Health Manager").