Yes, RMS is designed for that but as you can see the device is having a hard time connecting to it due to the network outage but usually it will automatically reconnect to the RMS server. Could you try disabling and enabling monitoring on the RMS side? Because in these such cases enabling and disabling RMS will do the trick or even just a reboot.
One thing you can do is to reboot the router through SMS Command a SMS command:
"router password" reboot
example: Teltonika123 reboot