If you have enabled the Connected Standby and face the issue about the new notifications not pushing after installed the Windows 10 Anniversary Update, try any of the methods to fix it.
However, many background activities of the apps are suppressed and that casue problem, such as you are unable to receive new notifications from mail, skype and others and the syncing is also not working in sleep mode. And the Anniversary Update (Build 14393 Version 1607 or later) always block some of the less-valuable apps, services and activities for improving battery life while keep your PC has key connectivity with inernet. Windows 10 and 8 has the Connected Standby feature to function your device in a low-power state and work more like a tablet or smartphone.