A/C compressor shutting off but

The A/C control has the choice of "on" or "auto" for the fan and we always keep it on "auto". I happened to hear the unit in the bedroom compressor cut off during the night last night, so I immediately turned the whole unit off as it is right by my side of the bed. We are hooked up at home right now so we didn't have both units running at the same time. I have not noticed it doing this before.

As far as we know these are the orginal units on this 2003 FW (we bought used) so they are 10 yrs old. They cool very well other than this happening last night.