There has been limited support for this hypothesis, and most of the others, because so many hypotheses make the same predictions that one can rarely conclude that a particular factor is at play unless one ignores all the other possibilities (which seems to be the standard practice.)
This paper from Proc.Roy.Soc.B. takes an interesting new tack, looking not at whether males that are shorter lived than their mates are taking more risks, but rather at whether their short-livedness can be explained by increased mortality during the season of risk taking.
Here is the abstract:
Male excess mortality is widespread among mammals and frequently interpreted as a cost of sexually selected traits that enhance male reproductive success. Sex differences in the propensity to engage in risky behaviours are often invoked to explain the sex gap in survival. Here, we aim to isolate and quantify the survival consequences of two potentially risky male behavioural strategies in a small sexually monomorphic primate, the grey mouse lemur Microcebus murinus: (i) most females hibernate during a large part of the austral winter, whereas most males remain active and (ii) during the brief annual mating season males roam widely in search of receptive females. Using a 10-year capture–mark–recapture dataset from a population of M. murinus in Kirindy Forest, western Madagascar, we statistically modelled sex-specific seasonal survival probabilities. Surprisingly, we did not find any evidence for direct survival benefits of hibernation—winter survival did not differ between males and females. By contrast, during the breeding season males survived less well than females (sex gap: 16%). Consistent with the ‘risky male behaviour’ hypothesis, the period for lowered male survival was restricted to the short mating season. Thus, sex differences in survival in a promiscuous mammal can be substantial even in the absence of sexual dimorphism.