DougS - I think that once the telomere has failed the DNA is too damaged to ever reproduce itself again. So the location of a specific gene or damage associated with it would be irrelevant. As I understand it (?) the telomeres themselves are not associated with the actual 'genes'.
I think that a significant sample of age related diseases are, however, related to this process. Once a cell has reached the limit of it's ability to duplicate itself, it remains in place in a 'damaged' condition. It is the accumulation of these damaged cells in our systems that manifests itself as age related disease.