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Many e-services are time-sensitive as the users request them for a specific time period. Such services need to be repeatedly offered to keep them constantly utilized. This paper studies winner selection strategies in a recurring auction for such time-sensitive e-services. We observe that because of uneven wealth distribution, the least wealthy bidders tend to drop out of recurring auction as they persistently loose. The bidders dropping out of an auction decrease competition and can cause a collapse of winning prices. We propose and evaluate a novel auction mechanism that enables bidder drop control. Compared to traditional auction mechanisms, ours increases revenue of the e-service provider and decreases loss of fairness of the e-service allocation.