What's the detailed version of your Exchange server?
Does this Inbox belong to a user mailbox, or other types of mailbox?
How do these users add and check the shared Inbox folder?
When does this issue begin? Did you make any modification before this issue?
Try to use the following command to search the missing message, and you can copy the search result to another mailbox:
Search-Mailbox -Identity <mailbox name> -SearchQuery {Subject:"<message subject>" AND From:<user name>} -TargetMailbox <mailbox name> -TargetFolder <folder name> -LogLevel Suppress
The SearchQuery parameter specifies a search string or a query formatted using KQL. For more information about KQL in Exchange, see Message properties and search operators for In-Place eDiscovery.
Please also check if any retention tag or retention policy is applied to the mailbox and folder:
Get-Mailbox <mailbox name> | Select Name, RetentionPolicy
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