Catalytic converter

I've got a question for you. Can a catalytic converter evenualy fail due to a vehicle not beeing driven enough for the converter to work properly. My 82 year old mother took her '92 jeep cheorkee sport in because the engine light came on. She was told that it was her converter and needed replacement. They told her that it failed because she didn't drive it enough for the system to heat up enough to work properly and so eventuly fail. They had replaced the converter aprox. 3 years before with a rebuild. She drives the Jeep mostly in intown traffic and it has just alittle over 58,000 miles on it. So, granted, she doesn't drive the heck out of it. But I sure have never heard of a catalytic converter failing for too little use. Can this possibly be on the up and up? Or might she be getting scammed? I've heard of failure due to too much heat but not the reverse. Any insight on this would be greatly appreciated. Thanks. Matt