I have a user with 80+ folders (not under the inbox), some with sub folders,  in the email account.  Mostly uses Outlook 2016 to manage email, but also has a iphone to check messages.  We noticed that her folders on SmarterMail Website (Web Mail) are empty, but they have messages in them on Outlook.  Clearly it's not syncing.   She is connected to the internet.  Her total mailbox size is pushing 5.6GB (yeah, I know...)

Is this an issue with the sheer volume of messages / mailbox size?

Does SM (or Outlook) timeout when attempting to sync that many messages?

She does not have any limit on mailbox size (again, I know.).  

We thought we would setup her mailbox to sync everything to the SM on the Server (vs. additional PST files on her HD) just in case her system crashed.  This has happened in the past and lost a lot of email -- some of which we were able to restore.  

Outside of telling her to delete a bunch of old emails, is there anything else that can be done?

A second issue, and I'm sure it's related, she experiences several times that new email appears on her iPhone 20-30 minutes before appearing on her computer (Outlook checks for messages every 5 minutes, her iPhone every 10).  Again, is this delay caused by Outlook attempting to sync a enormous amount of messages?