Hi Alexa,
FED3 will save the date/time after it's been set one time. Are you flashing the "SetClock" example and then flashing your FED3 control code?
You can find the SetClock and example programs in the FED3 library
examples within the Arduino IDE - installing from Aduino instead of Github will make sure you are using the
correct libraries, etc. See video on how to set clock
here.
If that's all fine, the behavior you're experiencing sounds like the coin cell battery (red arrow below) that powers the RTC might be bad - is your FED a few years old? That battery lasts ~3 years. It's a small CR1220, you will need to loosen the screws that secure the circuit board inside to replace it.
Post back if you figure it out! -Lex