Why do Politicians not solve social problems? One reason may be that such problems are difficult to solve, or that Politicians are incompetent. But there is another reason: in representative democracies, competent Politicians sometimes lack the incentive to solve problems to keep their enemies alive, in order to conserve an electoral advantage. This paper shows that reputational strengths can, to some extent, circumvent Politicians incentives not to address the problems. If the reputation of an incumbent Politician depends on the amount of reforms he implements, and positively affects his probability of being reelected, the trade-off between reputation and the need for enemies leads to an incomplete set of reforms, which can handle only a part of the problems. This mechanism might contribute to the explanation of the high degree of persistence of some social or economic diseases such as, specifically, public indebtedness.