We study platform markets in which agents arrive gradually, experience changes to their preferences over time, and are frequently re-matched. We introduce simple auctions specifically designed for such markets. Upon joining, agents select a status that determines the weight assigned to their future bids. Each match is then assigned a score that depends on the agents' reciprocal bids and status. The matches maximizing the sum of the bilateral scores are implemented. Under certain conditions, such auctions maximize profits, welfare, or a combination of the two. We use the results to shed light on the distortions due to platforms' market power.