We consider a decentralized two-sided matching market in which agents arrive and depart asynchronously. As a result, it is possible that an agent on one side of the market (a "buyer") identifies an agent on the other side of the market (a "seller") who is a suitable match, only to find that the seller is already matched. We find using a mean field approach that lack of knowledge about availability can create large welfare losses to both buyers and sellers. We consider a simple intervention available to the platform: limiting visibility of sellers. We find that this intervention can significantly improve the welfare of agents on both sides of the market; sellers pay lower application costs, while buyers are less likely to find that the sellers they screen have already matched. Somewhat counterintuitively, the benefits of showing fewer sellers to each buyer are greatest in markets in which there is a shortage of sellers.