I have been experiencing this issue too. On maybe 10% of iPads. Meraki build 45. ios 9.3.5. (in other words, the latest)
When manually forcing a check in that WORKS I see in the console log:
Oct 11 11:18:55 al-ipads76 mdmd[833] : (Note ) MDM: mdmd starting...
Oct 11 11:18:55 al-ipads76 mdmd[833] : (Note ) MDM: Network reachability has changed.
Oct 11 11:18:55 al-ipads76 mdmd[833] : (Note ) MDM: Network reachability has changed.
Oct 11 11:18:55 al-ipads76 mdmd[833] : (Note ) MDM: Push token received.
Oct 11 11:18:55 al-ipads76 mdmd[833] : (Note ) MDM: Received push notification.
Oct 11 11:18:55 al-ipads76 mdmd[833] : (Note ) MDM: Polling MDM server https://ios.meraki.com/apple_mdm/ios?org=129225 for next command.
Oct 11 11:18:56 al-ipads76 mdmd[833] : (Note ) MDM: Transaction completed. Status: 200
Oct 11 11:18:56 al-ipads76 mdmd[833] : (Note ) MDM: Server has no commands for this device.
Oct 11 11:18:57 al-ipads76 mdmd[833] : (Note ) MDM: mdmd stopping.
On iPads where the check in DOES NOT WORK I see:
Oct 11 11:23:56 al-ipads75 mdmd[229] : (Note ) MDM: mdmd starting...
Oct 11 11:23:56 al-ipads75 mdmd[229] : (Note ) MDM: Network reachability has changed.
Oct 11 11:23:56 al-ipads75 mdmd[229] : (Note ) MDM: Network reachability has changed.
Oct 11 11:23:56 al-ipads75 mdmd[229] : (Note ) MDM: Push token received.
Oct 11 11:23:56 al-ipads75 mdmd[229] : (Note ) MDM: Received push notification.
Oct 11 11:23:56 al-ipads75 mdmd[229] : (Error) MDM: Rejecting MDM push dictionary because it does not have the right magic string.
So "Rejecting MDM push dictionary because it does not have the right magic string." seems to be the key.
If someone can pass this by Meraki that would help. I'm not allowed to contact Meraki support.