Then it could be something blocking the connection with the GCM (Google Cloud Messaging) service.
Check the file C:\ProgramData\3CX\Instance1\Data\Logs\3CXDialer.log right after you try to make a call to an extension that should wake up with PUSH.
towards the end of the file you should see a line starting with {"registration_ids" : and in the next line you should see the response from the GCM service, ideally that should be GCM response: OK OK.
If you don't see that then possible reasons could be:
- Outbound traffic from the 3CX Server to the GCM service happens over ports 5228, 5229 and 5230, so make sure those ports are open for outbound traffic.
- Although I have yet to understand why this happens sometimes, but sometimes deleting the PUSH project and recreating it to get a new API Key and Project Number, inserting them into the Management Console and reprovisioning the phones again solves this issue.