If you use mail-extensions or our mail filter to automatically sort emails in folders, then the messages might not get transmitted via push services to your iOS device.
If you want to select folders, that are not the inbox, for automatic transmission via push, then you need to activate push for these folders manually.
Please go to “Settings”, then to “Mail, Contacts, Calendars”. Please click on “Fetch New Data” and choose the Exchange account, that you have connected with mailbox.org. Now you can see an overview of all IMAP folders in your e-mail account. Please tick the folders that you wish to synchronize automatically on your iOS device.