This article describes potential fixes for the issue when a shared Exchange Online email account folder, such as for an Exchange Resource Account, will not update or updates inconsistently. Some indications that you are experiencing this issue might be:
Folder synchronization issues, performance issues, and other problems occur if the number of folders per mailbox exceeds 500. Shared mailboxes and folders tend to bump into this performance limit more often than individual user mailboxes. Further, the way Outlook performs the connection to shared mailboxes compounds the issue. For detailed information regarding this issue, causes, and workarounds see Microsoft Support KB 3115602: Performance and Synchronization Problems.
There are some possible resolutions to the problem that are detailed in KB article 3115602: