If you were to search for the genetic mutation behind this mouse's disease, you wouldn't find it; there isn't one. These mice develop disease only because their telomeres are short, and having telomerase doesn't lengthen them right away.
These offspring have what we have called 'occult' genetic disease -- their genetic make-up is perfectly normal, but they still have the physical problems of their parents. This phenomenon could complicate the hunt for disease genes.