I think with these pukka DS3231 RTC chips it's a matter of luck if you get a good one.
I'm running one, temperature compensated crystal, over a long period, say a year, and displaying the results on an LCD.
One thing I do notice is that now and again it does a jump on the seconds of maybe 5 seconds. I don't know if it's the LCD or the RTC.
I keep some MSF ("atomic clocks") running and they are remarkably consistent and accurate.
I use either these or the phone clock to check the DS3231 and I have to say, that it keeps really good time within seconds over many months.
Some of the worst RTCs are in things like programmable thermostats from people like Honeywell and they lose minutes in months.
GPS is a good source of accurate time.
I have a bog standard antenna outside on a roof and use an XBee radio to transmit the data stream to inside the house.
GPS or MSF/DCF can be used to correct the DS3231 on a regular basis.
For a real clock fanatic, look at Brett Oliver's website for what can be achieved with time pieces.
Udo Klein (Blinkenlights) is a DCF77 expert with a library or code for Arduinos
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