In most home systems, losing internet affects remote monitoring, not basic power generation. The inverter usually continues to operate locally, provided the other necessary conditions are met. The exact behavior depends on the model and configuration.
The app may show old readings or indicate that the system is offline. This does not prove that generation has stopped. First, check the time of the last update and whether the router is working. Data storage and subsequent transmission depend on the equipment.
Services that use data from the internet, software updates, or remote automation may be unavailable. A separate issue is the loss of local communication with meters or other devices: this may trigger operating restrictions.
If the disconnection persists, contact the installer and provide the message displayed. Do not change electrical settings to restore Wi-Fi. An internet outage is different from a power outage on the grid.