I have a Sony ICFC218 Dream Machine Autoset Clock Radio which has a CR2032 lithium battery backup.
I've had it for about 10 years and have never replaced the battery.
If the power fails for any length of time, even days, it will come back with the correct time when power returns, no blinking display.
It even autosets for daylight time.
It's not radio controlled, I think it is just crystal controlled like a standard battery clock, since it does gain a few minutes a year, but that's acceptable to me.
That model appears to be no longer made but they may build an updated version.