Host life history and demography play important roles in host-pathogen dynamics, by influencing the ability of hosts and their pathogens to coexist. We introduce the concept of demographic competence to describe the ability of host populations to sustain endemic infectious disease. Hosts with high demographic competence are more likely to act as keystone hosts and constitute reservoirs of infection that can spill over into other species. We propose that the pace of host life history will interact with pathogen life history to influence demographic competence. Our models demonstrate that slow-living hosts (with high survival and low recruitment rates) have greater demographic competence than fast-living hosts (with low survival and high recruitment rates) for susceptible-infected disease dynamics, although this difference is reduced when populations of slow hosts are age structured. Demographic competence is generally greater among hosts with populations regulated by survival compared to reproduction, but this difference is smallest among slow life histories and reversed for some pathogens with frequency-dependent transmission. An association between pathogen life history traits and the demographic competence of faster-living hosts also has implications for trade-offs between pathogen virulence and transmissibility. Overall, we demonstrate how host life history traits can help predict wildlife reservoirs of zoonoses and the vulnerability of populations to disease-induced extinction.