Neuroevolution commonly uses speciation strategies to better explore the search space of neural network architectures. One such speciation strategy is through the use of islands, which are also popular in improving performance and convergence of distributed evolutionary algorithms. However, in this approach some islands can become stagnant and not find new best solutions. In this paper, we propose utilizing extinction events and island repopulation to avoid premature convergence. We explore this with the Evolutionary eXploration of Augmenting Memory Models (EXAMM) neuro-evolution algorithm. In this strategy, all members of the worst performing island are killed of periodically and repopulated with mutated versions of the global best genome. This island based strategy is additionally compared to NEAT's (NeuroEvolution of Augmenting Topologies) speciation strategy. Experiments were performed using two different real world time series datasets (coal-fired power plant and aviation flight data). The results show that with statistical significance, this island extinction and repopulation strategy evolves better global best genomes than both EXAMM's original island based strategy and NEAT's speciation strategy.