Most clock radios are synchronised to the mains, yes.
I have had ones before that have either lost or gained time, and I can only put it down to a faulty clock IC.
The IC has a 50 Hz / 60 Hz selector input which operates an internal counter and I suspect this part of the circuit goes AWOL.
Below is a link to the PDF for the TI TMS3450NL, a popular clock chip used in thousands of different designs.
Hope this helps.