I have an old (10-15 yrs) clock radio with a 9V battery backup to keep the time during power failures.
During the past week we have had two power outages which lasted over an hour, and in both cases the clock gained 5 minutes or so while the power was out. 
I can see how a weak battery could cause the clock to lose time, but is there an explanation for it gaining? It keeps time just fine as long as it’s running on normal power.
The clock normally uses the 60 hertz powerline frequency to keep time. When it goes on battery power, it runs from an internal oscillator. Since the point of using the powerline frequency is to avoid having an expensive (by the penny pinching standards of the manufacturer) crystal oscillator, they’re not about to build on in for use when the power fails.
To generate the 60 hertz signal when the power drops out, they use a simple resistor/capacitor oscillator. Since these parts have typical tolerances of 5% (resistors) and 20% (capacitors,) it would be a wonder if the clock kept good time during a power failure. The tolerances (which are also affected by temperature, humidity, and other things) can combine to give you a clock that runs too fast or too slow - or when you are terribly lucky - be just right.
Unsolicited plug here for “Atomic Clock” clock radios, the kind that pick up a signal from the US Atomic Clock in Colorado to set themselves. Unless you’re in an area where the signal is too weak, i.e., too far away from Colorado, they are fantastic. We get mini outages and brownouts all the time in Austin, especially in summer, and I love having one clock in the house that’s almost guaranteed to be spot on correct anyway. I hope eventually to replace all the clocks in the house with atomic ones.
Clocks havn’t used voltage occolation for time keeping for a long time, quartz crystals are far more accurate and cheap. My wag is that the battery is not supplying the proper voltage to keep the correct time. And I have noticed too that clocks always run fast, by almost the same amount when running on battery power, requreing the person to go through neadly 24 hrs to re-set the time. I wish they would run slow.
That’s what my alarm clock is - a battery powered DCF-77 that picks up the signal from a service here in Germany.
Nice little gadget - they just build them too cheaply. I’ve killed two already just by knocking them off of the bed stand at some ungodly hour of the morning when the alarm rang.
Every battery-backed clock-radio I’ve had gains time like mad when the power’s off.
I suspect the makers err on the side of fast so when the alarm goes off in the morning, you’ll be up earlier than intended, rather than late, causing you to miss the train, be late for work, etc and be thinking all day long about that good-for-nothing clock that caused you to be late.
Mine does this too; my WAG was what ** Mort Furd ** seems to be confirming.
Mine runs fast also. I bet gotpasswords is right - it would be smarter to design to run fast. I would suspect the backup power supply is totally different, and with the prices of these clocks it would not be worth it to put in the circuitry for high accuracy under battery backup conditions.
kanicbird - that’s why I only buy clock radios with forward and reverse buttons! Forget about power failures - setting the alarm backwards is a real pain, as is going through the whole cycle if you go too far in setting the time.
Most alarms can be set to 12 (midnight) by pressing the hour and minute button at the same time (along with the alarm button)
But a backwards button is well worth it.