If a mutation occurred in an individual such that it would not age, while everything else remained the same, that individual would have more reproductive opportunities and so would its offspring, but there would still be differential success, that is not all individuals would reproduce at the same rate. So you would still have reproduction, heredity and differential reproductive success. So evolution would continue. The fact that all creatures age suggest there is some fundamental trade off between longevity and other types of fitness.
I like David Sinclair's idea that while DNA can be considered digital data, copying it is an analog process and we end up with copies of copies of copies, each a little worse than the previous one, while DNA is still intact.
It sounds too simple to be true, but it's an interesting information theoretical based hypothesis.
