retain values after power down

Is there a way to have the MCU detect a drop in voltage (say across a large power cap/5V supercap) giving it enough time to write to EEPROM if say Voltage <2.5V and then goes to sleep till voltage >4.5 again for example?

Found this:
Low Voltage Detector IC

So it basically Outputs low when Vsupply <3V and high when Vsupply>3V.
An external interrupt pin could be used to detect the FALL.
For example, saving to EEPROM and sleeping on a FALLING edge of the INT pin.

Any clarify this as a good idea or is there a "better" MCU only option?