The proliferation of mitochondrial DNA (mtDNA) with deletion mutations has been linked to aging and age related neurodegenerative conditions. In this study we model the effect of mtDNA half-life on mtDNA competition and selection. It has been proposed that mutation deletions (\(\text {mtDNA}_{del}\)) have a replicative advantage over wild-type (\(\text {mtDNA}_{wild}\)) and that this is detrimental to the host cell, especially in post-mitotic cells. An individual cell can be viewed as forming a closed ecosystem containing a large population of independently replicating mtDNA. Within this enclosed environment a selfishly replicating \(\text {mtDNA}_{del}\) would compete with the \(\text {mtDNA}_{wild}\) for space and resources to the detriment of the host cell. In this paper, we use a computer simulation to model cell survival in an environment where \(\text {mtDNA}_{wild}\) compete with \(\text {mtDNA}_{del}\) such that the cell expires upon \(\text {mtDNA}_{wild}\) extinction. We focus on the survival time for long lived post-mitotic cells, such as neurons. We confirm previous observations that \(\text {mtDNA}_{del}\) do have a replicative advantage over \(\text {mtDNA}_{wild}\). As expected, cell survival times diminished with increased mutation probabilities, however, the relationship between survival time and mutation rate was non-linear, that is, a ten-fold increase in mutation probability only halved the survival time. The results of our model also showed that a modest increase in half-life had a profound affect on extending cell survival time, thereby, mitigating the replicative advantage of \(\text {mtDNA}_{del}\). Given the relevance of mitochondrial dysfunction to various neurodegenerative conditions, we propose that therapies to increase mtDNA half-life could significantly delay their onset.