Although demographic studies have failed to find evidence of aging in certain animal species, classic evolutionary theories of aging struggle to explain how evolution could favor agelessness in such cases. Here, we develop mathematical models of the disposable soma theory to identify conditions in which agelessness would be evolutionarily favored. For any given type of damage that could accumulate and cause age-accelerating mortality risk, we find that evolution could select for its complete removal if the mortality risk it poses is severe enough and its repair does not pose too large of a penalty to reproduction. Environmental factors such as extrinsic mortality and the form of population density-dependent regulation also play a large role in determining the optimal rate of aging and whether agelessness should be evolutionarily favored. However, in a system with multiple sources of damage and multiple independent repair processes, avoiding aging is rarely evolutionarily favorable. Pleiotropic repair processes, such as those that could be present in asexual fissioning organisms, make agelessness more likely but do not guarantee it. Our results indicate that agelessness could be favored by evolution in narrow contexts but that multiple types of damage and repair make agelessness unlikely to arise in sufficiently complex organisms.