The eMon Energy Monitor can operate without a permanent internet connection. It can store 10 years of data in its internal memory. Once it is connected it will upload all data since its last connection to your server. You will still be able to use the device internal graphical system.
Without a connection to a WiFi Access Point the eMon Energy Monitor will automatically switch mode and becomes an WiFi Access Point itself that you can connect to with your phone or PC.
You can also set up your own local servers with monitoring software and dashboards such as InfluxDB/Grafana or emoncms. A Raspberry Pi will have enough power.