We consider a model in which consumers wish to buy a product repeatedly over time, but need to engage in costly search to learn prices and find a product that matches them well. The optimal search rule has two reservation values, one for newly-searched products, and another for products that were searched in the past. Depending on the search cost, firms either keep price steady over time, or gradually raise price to take advantage of a growing pool of high-valuation repeat customers. The model generates rich search and purchase dynamics, as consumers may optimally “stagger” search over time, initially trying different products, settling on one and buying it for a while, before choosing to search again for something better. We also show that consumers may be better off when firms can offer personalized prices based on their search history.