Demystifying Hybrid Free/Busy: Finding errors and troubleshooting

For migrations, same process, check the IIS logs and HTTPProxy logs for EWS or Autodiscover if you are using it and depends exactly where you have the failure at the timestamp of the failures: 
$stats = get-moverequeststatistics <user X> -IncludeReport 
$stats.Report.Failures | FT timestamp, failuretype

Check these resources:
Troubleshooting Failed Migrations - Microsoft Community Hub
Digging Into Hybrid Migration Move Report Data - Microsoft Community Hub

Make sure ExchangeGuid / ArchiveGuid on the Faulty user is matching onpremises remote mailbox attributes. Make sure we don't have anything weird in Exchange online regarding primary mailbox and archive, should be only one mailbox /archive. You can use Get-MailboxLocation -User <user X> | FL to see all Mailbox Location types in EXO and their Guids. In Exchange Onpremises, Get-Recipient <user> |FL and Get-RemoteMailbox <user> |FL