The object of this paper is to investigate the long-run behaviour of rent-seekers in a situation where they incur negative expected payoffs due to increasing returns to rent-seeking expenditures. To this end, we embed the one-shot rent-seeking game presented by Tullock (1980) in the war-of-attrition framework. In this multi-period setting, each player not only determines his or her rent-seeking expenditure but also chooses a mixed strategy on whether to stay in or exit from rent-seeking competition in each period.