In which situation will a mutation not persist or spread in a population?

A situation where in the mutation won’t spread or to persist in a population is when the population has not evolve itself, because if it has evolved, meaning alleles may change—contributing to the changes and could help in spreading mutations in a population.

the principles and empirical processes of discovery and demonstration considered characteristic of or necessary for scientific investigation, generally involving the observation of phenomena, the formulation of a hypothesis concerning the phenomena, experimentation to test the hypothesis, and development of a conclusion that confirms, rejects, or modifies the hypothesis.