Question

can an organism naturally repair a mutation

Answer 1

If a mutation occurs during replication, several replication coupled repair system recognizes and repairs it (BER and NER).

If a mutation occurs due to exposure to a chemical, post-replication associated repair system recognize and repair it (BRCA, BLM, and NBS1).

However, once the mutation is established in one generation of an organism, its frequency in the population depends upon its relative fitness and is subjected to natural selection.

In such cases, the organism cannot directly reverse a mutation. Just like mutations, reversions are also random.