You don't have permission to sync with this server exchange 2010

This error is caused by the maximum Mobile Phone limit (10 device)  in Exchange 2010.

You can increase this limit by using Throttling policy.

First Create new throttling policy.

New-Throttlingpolicy "Increased ActiveSync Devices1" -EasMaxDevices 

600 -EasMaxConcurrency 20

 -EasMaxDevices 20 (Maximum mobile phone limit)

 -EasMaxConcurrency  (Maximum  concurrent device that will sync.)

Then assign this policy to user.

Set-Mailbox username -ThrottlingPolicy "Increased ActiveSync Devices1"

Check if Policy applied to mailbox

Get-Mailbox username -ThrottlingPolicy | FL