That is why I got the hell in with the nice clock that ate new batteries in a month. I swapped it with an older one which runs a year or more on a cell ( though there is one at home which is still using the same AA cell from 5 years ago, still not leaking at last check) and power it off a 12V standby source. 14Ah of cell capacity ( more or less at this low load, and dropout will be at a level terminal to the cell recovering anyway) will run it fine for any power failure short of a 6 month outage. Also discovered that clock oscillators are really dependant on cell voltage, this one gains time at 1V6, tried 1V2 and it keeps time perfectly.
I have some NiCd cells in an alarm clock, been in there for over a decade and still do the job. Originally used a CR2032 cell, but got modified a little, now has a 3V regulator using a AC129 PNP germanium transistor, simply because it uses the 3V rail as switch common, and i disliked the slide switch, so put in a small BCD switch instead. My alarm clock, has been running for nearly 30 years. Ricoh made a good module for sure.