Hi @Michael Adams ,
What's the specific version and license of your Outlook 2019? Please first ensure that you have updated to the latest version of Outlook client.
Also, as I know, the online archive feature is available to some specific version of Outlook, it's recommended to follow this document to check if your Outlook 2019 could meet the requirements of license.
If that's not your case, based on my research, I found a related document about How to troubleshoot an Exchange Online Archive mailbox that is not displayed in Outlook, please follow it to check if that could work for you.
If the response 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.