I just migrated to a new computer and imported my email from Outlook 2007 on old computer to Outlook 2013 on new one. After successful importing, inbox messages older than 120 days started disappearing. I re-imported, had them all back for a little while, then they disappeared again. I don't have auto-archiving on, and they are not going into an archive or into trash; they just vanish. When they are going away, I can see the count of items in my inbox dropping, and the bottom of the Outlook screen shows "Inbox synching" or something similar.
How can I stop this from happening?