Empty RTC battery

Hi all, I’m working with Nextion Enhanced & Intelligent series displays from 3.2" to 7". I’m searching for an easy way to implement a “RTC battery fault” in my project.
Now I’m checking the month=01 and day=01 to store the year in eeprom only if it’s “last_year+1”, then I check it every power_up of system. For the rest of days and month in a year I uplight a “battery fault” flag if eeprom year is diffent from RTC yesr. It’s working, but if I’ve no power-down I can’t catch a battery fault.
While power is on, the RTC is working properly, and the battery status is unknown: any ideas to implement a control on this?
Thanks in advance for any ideas on this!!