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Rexes (at least most rexes) will lose their leaves in winter. Pick off dead and diseased leaves to keep mildew at a minimum. Do not water heavily during these times ESPECIALLY if the room is cool. You have to give them enough water to keep the rhizomes plump but not too wet else the rhizomes will rot. Not an easy task. Humidity chambers (aquarium comes to mind) may help in this endeavor.

I lost several last year despite being very careful on watering but the ones I lost were in a much cooler room than the ones I did not lose. I actually believe you can put them in a darker cool room (like a garage) and not water them for a month or longer and still be okay (I have done this before but it's hard to gauge when to water).

Almost all of mine this year are doing fine because I have them all under lights and the room is a lot warmer than last year.

Butch