EXACT SAME PROBLEM with us. We have found through the ExRCA testing page (testconnectivity.microsoft.com) that the "Exchange Web Services synchronization, notification, availability, and Automatic Replies" fails for all the affected users with errors in the Notification Events section.
Since those push notifications are failing, iOS and Outlook 2011 for Mac aren't aware of new items, so they don't do the background refresh. That's why you need a manual fetch to bring in the new items. I don't know if the servers are overloaded or misconfigured, but that's where the failure is happening.
Here's the relevant failure info from the ExRCA test:
Getting subscription events and confirming that the expected events exist.
Events couldn't be retrieved or confirmed.
Additional Details
No notifications were returned.
Last EWS request:
<Trace Tag="EwsRequest" Tid="55" Time="6/6/2013 3:58 PM:55Z" Version="15.00.0692.000">
<?xml version="1.0" encoding="utf-8"?>
<soap:Envelope xmlns:xsi="www.w3.org/.../XMLSchema-instance" xmlns:m="schemas.microsoft.com/.../messages" xmlns:t="schemas.microsoft.com/.../types" xmlns:soap="schemas.xmlsoap.org/.../">
<soap:Header>
<t:RequestServerVersion Version="Exchange2007_SP1" />
<t:TimeZoneContext>
<t:TimeZoneDefinition Id="Pacific Standard Time" />
</t:TimeZoneContext>
</soap:Header>
<soap:Body>
<m:GetEvents>
<m:SubscriptionId>JgBieTJwcjA0bWIwMTUubmFtcHJkMDQucHJvZC5vdXRsb29rLmNvbRAAAAAcL8xvKf86QrBhTjJ+tWV3i5hm4eUw0Ag=</m:SubscriptionId>
<m:Watermark>AQAAAOQxgDhpcn5HvGPBFWLNclkC048CAAAAAAA=</m:Watermark>
</m:GetEvents>
</soap:Body>
</soap:Envelope>
</Trace>
Last EWS response:
<Trace Tag="EwsResponse" Tid="55" Time="6/6/2013 3:58 PM:56Z" Version="15.00.0692.000">
<?xml version="1.0" encoding="utf-8"?>
<s:Envelope xmlns:s="schemas.xmlsoap.org/.../">
<s:Header>
<h:ServerVersionInfo MajorVersion="15" MinorVersion="0" MajorBuildNumber="702" MinorBuildNumber="18" Version="Exchange2013" xmlns:h="schemas.microsoft.com/.../types" xmlns="schemas.microsoft.com/.../types" xmlns:xsd="www.w3.org/.../XMLSchema" xmlns:xsi="www.w3.org/.../XMLSchema-instance" />
</s:Header>
<s:Body xmlns:xsi="www.w3.org/.../XMLSchema-instance" xmlns:xsd="www.w3.org/.../XMLSchema">
<m:GetEventsResponse xmlns:m="schemas.microsoft.com/.../messages" xmlns:t="schemas.microsoft.com/.../types">
<m:ResponseMessages>
<m:GetEventsResponseMessage ResponseClass="Success">
<m:ResponseCode>NoError</m:ResponseCode>
<m:Notification>
<t:SubscriptionId>JgBieTJwcjA0bWIwMTUubmFtcHJkMDQucHJvZC5vdXRsb29rLmNvbRAAAAAcL8xvKf86QrBhTjJ+tWV3i5hm4eUw0Ag=</t:SubscriptionId>
<t:PreviousWatermark>AQAAAOQxgDhpcn5HvGPBFWLNclkC048CAAAAAAA=</t:PreviousWatermark>
<t:MoreEvents>false</t:MoreEvents>
<t:StatusEvent>
<t:Watermark>AQAAAOQxgDhpcn5HvGPBFWLNclkC048CAAAAAAA=</t:Watermark>
</t:StatusEvent>
</m:Notification>
</m:GetEventsResponseMessage>
</m:ResponseMessages>
</m:GetEventsResponse>
</s:Body>
</s:Envelope>
</Trace>