When syncing to Exchange 2013, an issue can arise where mailboxes do not sync and the MAgE log shows:
Error System.Net.WebException: The request failed with HTTP status 507: Insufficient Storage.
Corruption has been ruled out and pre-requisites have been double checked.
Refer to the following Microsoft article to consider increasing the EWS Client-specific message size limits in the web.config file of the Exchange servers handling any EWS requests. The maxRequestLength parameter could also be a factor.
It is recommended that one should consult with Microsoft if there is any uncertainty about or resulting from changing these parameters.