Have you received some NDR? Error messages?
I want to confirm that the administrator mailbox can send and receive emails through outlook or OWA?
Compare administrator with test user in configuration, In addition to administrative privileges.
In addition, I recommend to configure a new ActiveSync device with problematic account.
If it works fine, it indicates that profile setting on current ActiveSync device is corrupt, we need to remove the account profile and reboot mobile device, then re-configure it again for testing.
If it remains existing in new device, please try to restart IIS or recycle MSExchangeSyncAppPool on Exchange server.