I can understand a mechanical system falling out of time, but my microwave clock is gradually *gaining* time, and I’m pretty sure it doesn’t have a mainspring.
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ELI5 version: time is kept by counting how much a rock shakes, time is lost by the rock not shaking as fast as it is expected to shake
ELI20: time for digital clocks is kept by a quartz crystal which has a known frequency, of course not everything is perfect, so even a variation of 1hz causes a daily shift of a few seconds
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Digital clocks still have a timekeeping mechanism inside them, it’s just very small and modulated by crystals and microchips instead of by gears and springs. Where a mechanical clock uses an escapement mechanism, a digital clock counts the regular vibrations of an electrically-charged quartz crystal to tell time. Slight variations in the manufacturing process may result in vibrations that are slightly imprecise, making the clock slowly gain or lose time.
There’s two reasons, both very seperate, and both very real, and they can work together, or oppositely.
The first is, as many have said, the power cycle. US power is supposed to be at 60Hz, so the clocks get their timing off that somewhat. Elsewhere it’s 50hz, like in Europe, where a dispute in the Balkans 4 years ago caused clocks to [lose about 6 minutes](https://www.theguardian.com/world/2018/mar/08/european-clocks-lose-six-minutes-dispute-power-electricity-grid) in total because of frequency mismatches.
The second is even simpler. most clocks are REALLY CHEAP and really s**t. The clock in your PC? it’s less accurate than a $5 wall clock powered by a AA. If they lose a minute over 5 months, who cares? In a lot of the world you’re going to be changing it anyway for daylight savings/summer time twice a year, and you really won’t notice if its had 90 seconds of drift over 6 months (which is half a second a day). And that assumes your power is perfect, and you don’t have a blip that’ll reset it anyway. So why are they going to spend money on making sure it’s all that accurate?
Real atomic clocks measure time through the vibration of a cesium atom, these are insanely accurate, and we actually use a certain number of cesium atom vibrations as a standard for a second (9,192,631,770), so these are technically always 100% correct
Your digital alarm clock measures time through some other mean which may not be as accurate as the literal standard of what a second is defined as, so naturally these may eventually get out of sync.
Clocks on your smartphone, or computer don’t go out of sync because these are synced with some kind of time server elsewhere that is either run by an atomic clock, or synced by some other mean.
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