Some users have reported that they only receive emails to their mobile devices when they open Outlook on their local computer.  This seems to happen after a security update for example AVG program update.  To resolve this issue enable proactive scanning.

Enabling proactive scanning

Microsoft Exchange proactive scanning can be enabled on Mailbox servers. With proactive scanning, Mailbox servers that contain public folder databases scan files as they are posted to the server. Proactive scanning also causes a scan of messages in the Sent Items folder in mailbox databases.

By default, proactive scanning is disabled. However, because content posted to a public folder database is usually not routed through a Hub Transport server, in order to ensure that the content is scanned before it gets to the store, it is recommended that you enable proactive scanning for public folder databases. Scanning material as it is posted to the public folder database also prevents download delays when the content is accessed.

You can enable proactive scanning in one of the following ways:

Set the following Exchange DWORD registry value to 1:

HKEY_Local_Machine\System\CurrentControlSet\Services\MSExchangeIS\VirusScan\ProactiveScanning

By default, this registry value is set to 0 (proactive scanning is disabled).