Hi Climbguy3 and Sean,
Based on your description, I understand Outlook 2011 and iPhone don't download emails automatically. However, OWA and Outlook 2010 for Windows have no problems.
To narrow down the root cause of this issue, I would like to confirm the following information:
1. How do you set up Office 365 on Outlook 2011 and iPhone?
2. Can the user send emails via Outlook 2011 and iPhone without clicking the send/receive button? Does the emails stay in Outbox folder?
3. Please also check the send/receive settings.
Regards,
Jerry Cen