Do you have any examples of a species rendered extinct by a plague in nature?
How would we know? A pandemic should kill in a generation or two, leaving essentially no fossils (and if there were fossils, would we notice unless it was some sort of weird bone-distorting disease? or even then...), so the deep historical record would not help much. The human historical record is very sketchy since germ theory is so new and so many anciently-recorded species are of uncertain identification (think of all the plants and insects in the Bible we don't know what they actually are), and when humans are competent to record data about wild diseases and plagues, it's generally because they're part of the problem: Tasmanian Devils are being killed off by a nasty communicable cancer (population cut by 70% since 1996, Wikipedia says), but maybe their vulnerability is just due to human-caused stress or something.
Recent observations, not fossil record or ancient history. And extirpation of a connected population from its (substantial) range is an OK proxy.
The FHI's mini advent calendar: counting down through the big five existential risks. The fourth one is an ancient risk, still with us today: pandemics and plagues.
Pandemics
Current understanding: high
Most worrying aspect: the past evidence points to a risky future
The deathrates from infectious diseases follow a power law with a very low exponent. In layman’s terms: there is a reasonable possibility for a plague with an absolutely huge casualty rate. We’ve had close calls in the past: the black death killed around half the population of Europe, while Spanish Influenza infected 27% of all humans and killed one in ten of those, mostly healthy young adults. All the characteristics of an ultimately deadly infection already exist in the wild: anything that combined the deadliness and incubation period of AIDS with the transmissibility of the common cold.
Moreover, we know that we are going to be seeing new diseases and new infections in the future: the only question is how deadly they will be. With modern global travel and transport, these diseases will spread far and wide. Against this, we have better communication and better trans-national institutions and cooperation – but these institutions could easily be overwhelmed, and countries aren’t nearly as well prepared as they need to be.