Hi James,
For your question, please run below command to check the setting for those problematic resource mailbox:
Get-CalendarProcessing "Resource Mailbox" | FL
Ensure the value of below parameter:
AutomateProcessing: AutoAccept
AllowConflicts: False
If it's a recurring meet request, please ensure the value of ConflictPercentageAllowed and MaximumConflictInstances.
More details about "Automatic Processing of Recurring Meeting Requests with Conflicting Instances", for your reference:
https://blogs.technet.microsoft.com/exchange/2011/02/07/automatic-processing-of-recurring-meeting-requests-with-conflicting-instances/
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Allen Wang
TechNet Community Support
