Arthur,
We typically recommend moving the subfolders out of the Inbox and keep in the in the root level. There have been several reported issues with Outlook 2013, and 2010 with subfolder under the Inbox failing to synchronize via IMAP and EAS. This doesn't appear to be an isolated incident with SmarterMail servers as it has been reported across several server types.
Please refer to the following KB article for more information: https://portal.smartertools.com/kb/a2850/support-for-folders-within-your-inbox.aspx
I hope this helps !