Customer option: use an uninterruptible power supply
Choose a unit for the measured power draw of the complete setup and the running time the household needs. The VA figure alone does not guarantee a particular runtime.
Every item needed to make the internet connection work must be connected to the UPS. Powering only the phone will not keep the service working.
Actual running time depends on the equipment, battery age and battery condition. Test the complete setup rather than relying on the figure printed on the box.