Which  enzymatic  mutation  is  responsible  for immortality of cancer cells?
With respect to cancer, when tumor cells divide rapidly their telomeres often shorten.
Such telomeres  (usually detected in leukocytes because of ease of obtaining them) have been implicated as a risk  factor for many, but not all, solid tumors (eg, breast cancer). 
Short telomeres appear to be of predictive value regarding the progression of chronic inﬂammatory diseases (such as  ulcerative colitis and Barrett esophagus) to cancer.
The activity of telomerase, the main enzyme involved in synthesizing telomeres, is frequently  elevated in cancer cells, providing one mechanism for overcoming telomere shortening. 
Selective  inhibitors of telomerase have been considered as possible drugs for treating cancer, but have not as  yet been translated into successful clinical usuage.

Key Concept:
Telomerase is the main enzyme that is seen elevated in cancer cells.
Ref : Harper’s illustrated biochemistry, 31st edition.
DNA reverse transcriptase
RNA polymerase
Telomerase
DNA polymerase