This paper deals with a two-person zero-sum game called search allocation game (SAG), in which a searcher and a target participate as players. The searcher distributes his searching resources in a search space to detect the target. Searching resources are durable so that their effectiveness lasts for a while. On the other hand, the target moves around in the search space to evade the searcher. There have been so far few researches taking account of the durability of searching resources. We develop two linear programming formulations to solve the SAG with durable resources and we find an optimal strategy of distributing searching resources for the searcher and an optimal moving strategy for the target. We also analyze influences of the durability of resources on optimal strategies by some numerical examples.