Nuclear decay being a chaotic process and all.
So-called "atomic clocks" utilize the RF absorption of various isotopes, typically Cesium or Rubidium. Heated to a vapor in a sealed chamber, the vapor is excited by a microwave RF source, and at a highly specific frequency, the vapor absorbs the RF energy. This phenomenon is used as part of a feedback loop to keep an electronic oscillator disciplined to whatever frequency is desired.
Atomic clocks won't work without electrical power, and would be subject to all the same physical rust and breakdown as other electronic devices over the years.