Hi Bart,
It’s normal behavior for cellular network. If your device does not have any network’s activity, it will enter to “RRC Idle” mode. With this mode, you can not ping to your device from outside.
It looks like that your private network sets up 30s for inactivity_timer. If you want, you can increase this parameter of your network.
You can use AT!GSTATUS? to show your device in “RRC_Idle” or “RRC_Connect”.
Your device is only reachable if it is in RRC_Connect.
To enter to “RRC_Connect”, it has to start connection or start the Tracking Area Update.
The Tracking Area Update timer could be configured on your network also.
Note that: when the device is in “RRC_Connect” and you make a ping to device, it will never enter to “RRC_Idle”.
Hope it can help.
Thanks,