In 2018, Ferrari et al. wrote a paper called "Phase Transition for Infinite Systems of Spiking Neurons" in which they introduced a continuous time stochastic model of interacting neurons. This model has a parameter $γ$, corresponding to the rate of the leaking times of the neurons and, as the title says, it was proven there to present a phase transition phenomenon with respect to this $γ$. Here we prove that this model also exhibit a metastable behavior. By this we mean that if $γ$ is small enough, then the re-normalized time of extinction converges toward an exponential random variable of mean 1 as the number of neurons goes to infinity.