Abstract In many species, male lifespan is shorter than that of females, often attributed to sexual selection favouring costly expression of traits preferred by females. Coevolutionary models of female preferences and male traits predict that males can be selected to have such life histories; however, this typically requires that females also pay some costs to express their preferences. Here we show that this problem diminishes when we link coevolutionary models of costly mate choice with the idea of stamina. In our model, the most successful males are those who can combine high attendance time on a lek — or, more generally, tenacious effort in their display time budgets — with high viability such that they are not too strongly compromised in terms of lifespan. We find that an opportunistic female strategy, that minimizes its costs by mating with highly visible (displaying) males, often beats other alternatives. It typically resists invasion attempts of genotypes that mate randomly in the population genetic sense, as well as invasion of stricter ways of being choosy (which are potentially costly if choice requires e.g. active rejection of all males who do not presently display, or risky travel to lekking sites). Our model can produce a wide range of male time budgets (display vs. self-maintenance). This includes cases of alternative mating tactics where males in good condition spend much time displaying, while those in poor condition never display yet, importantly, gain some mating success due to females not engaging in rejection behaviours should these be very costly to express. Significance statement In many species, males spend much time and energy on displaying to attract females, but it is not always clear what females gain from paying attention to male displays. The tradition in mathematical models attempting to understand the situation is to assume that random mating is the least costly option for females. However, random mating in the population genetic sense requires females to behave in a manner that equalizes mating success between displaying and non-displaying males, and here we point out that this is biologically unlikely. Opportunistically mating females can cause males to spend much of their time budgets displaying and will shorten male lifespans in a quality-dependent manner.