Hi @Neil Jones ,
What is the version of your exchange server? How many users are facing this issue?
Based on the event log 2004, I have done some research, most of them are talking about OWA issue not outlook connectivity issue.
Could you get returned certificate via running command Get-ExchangeCertificate -Thumbprint 0271xxxxxxxxxxE044F968F068B14B8 | Format-List?
If you cannot find the certificate, you could have a try to follow these steps in the blog to recreate a certificate to authenticate and then check if this issue continues.
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About event log 1009, you can safely ignore these logged events, which is mentioned in the article: 1009 errors flood Application log for lagged database copies in Exchange Server 2016
For further troubleshooting, you could run EXRCA to test outlook connectivity and you will get more details.
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