The car I was looking at went away so I'm off the market for now. Yes, I have SDS.

I'm thinking the cause for smart keys becoming unsynced is a low battery. If the read , response, write sequence is interrupted the key will become scrambled. I've worked on various cars that would crank all day if you wanted to but the voltage while cranking would drop far enough resulting in loss of clock , radio presets and sometimes a crank / no run condition. This occurs when a cell is shorted turning a 12 V battery into a 10 V battery with capacity left unaffected.