The cryogens boil off at a pretty consistent rate no matter what, but the recovery/recompression systems do require power. So once power is cut, any boil off isn’t recovered.
Superconducting magnets (like in MRIs) can run effectively forever when at the right temperature. Turning them off requires a complex process of draining off that current slowly and carefully so that the magnet isn’t damaged. Hard to do on a normal day, and profoundly harder if there’s no power.