When syncing from a live mailbox using IMAP, any changes to the state of the mailbox after the sync has started will affect the actual mails being synced.
For example, if new mail arrive after a sync request has started, they may not get synced. Similarly, mail deleted or moved between the start and end times of a sync request may not get synced.
In addition, in some rare cases, the conversion tool may not be able to migrate certain mail due to their structure. Such mail will be skipped.