Thanks for the question, and welcome to Apple Support Communities.
It sounds like you are not receiving push notifications due to a proxy setup on your Wi-Fi network. The following provides more information:
Devices using APNs need a direct connection to Apple's server. If a device is unable to connect using cellular data, it will attempt to use Wi-Fi if available. If there is a proxy server on the Wi-Fi network, the device will not be able to use APNs, because APNs requires a direct and persistent connection from device to server.