A popular approach in the design of evolutionary algorithms is to integrate local search into the random search process. These so-called memetic algorithms have demonstrated their efficiency in countless applications covering a wide area of practical problems. However, theory of memetic algorithms is still in its infancy and there is a strong need for a rigorous theoretical foundation to better understand these heuristics. Here, we attack one of the fundamental issues in the design of memetic algorithms from a theoretical perspective, namely the choice of the frequency with which local search is applied. Since no guidelines are known for the choice of this parameter, we care about its impact on memetic algorithm performance. We present worst-case problems where the local search frequency has an enormous impact on the performance of a simple memetic algorithm. A rigorous theoretical analysis shows that on these problems, with overwhelming probability, even a small factor of 2 decides about polynomial versus exponential optimization times.