First lets fix this:
likely due to the propensity of pathogenic organisms to adapt in such a way that they actually don't kill their host!
This is unlikely and flat wrong with respect to the black plague. Microbes generally don't evolve to be less lethal. The microbial world is fairly simply, they do whatever works to reproduce more effectively. Caring about where their nutrition comes from is about the furthest consideration conceived by their short existences.
Immune systems in a similar respect are equally simple, they kill whatever tries to grow where it shouldn't. In many illnesses it is not actually the pathogen itself that kills the host but the immune systems amplified response to the foreign intrusion that ultimately kills the host. Fevers aren't caused by a bacteria they are an immune response in an effort to kill the bacteria.
This brings us to why subsequent outbreaks of a pathogen are less devastating in ancient populations. Previous outbreaks killed off the immunologically weak members of the populace while surviving members passed on both resistant genes and antibodies to the next generation. So in subsequent outbreaks the pathogen is now dealing with immune systems that are more versed in how to deal with the pathogen. This results in both less fatalities as well as less dramatic manifestations of trademark symptoms.
Now for your actual question:
What mechanisms exist that might have made a subsequent outbreak of Yersinia pestis more virulent and more deadly that those that preceded it?
Pathogens can evolve certain changes in their structure that make it more difficult for white blood cells to identify them. This can increase the time between which a pathogen reaches a criticality needed to infect other members of a species and the time at which symptoms present themselves. Similarly, the pathogen can also evolve structures that make it more transmittable like being able to survive in an exposed environment or sticking to surfaces.
As stated before, simply existing can cause the immune system to kill itself. By being identifiable to the immune system but unkillable the immune system can amplify and amplify till it kills itself. Though that isn't the only means, like any good domineering organism, generalization is key. Being able to spread, adapt to different conditions, and exploit new resources is the key to success. For pathogens this means being able to conquer different tissues/organelles. Encephalitis is condition caused when an infection has compromised the brain. This is one of many means where an infection can directly kill the host as it eats away at brain cells eventually terminating the very controls that keep the body moving.
To be worse all Yersinia pestis, or any pathogen really, has to do is evolve traits that enable some of the above outcomes. This is generally hard to achieve when the host population is concurrently adapting to its changes. This brings us back to the first point and highlights this cyclical process of adaptation and why the first epidemic is worse than subsequent outbreaks, because the first one is new and unchallenged. I do now want to point out that just because the pathogen appears less deadly does not mean it is.
Did It Become Cuddlier?
HECK NO! If you understand the fact that the bubonic plague still exists today and actually look at plague maps of Europe and Asia over time you might notice What is reported as 3 different plagues isn't necessarily 3 different plagues but really the same plague just evolved each time. See if you pine over maps of Europe, Asia, and Africa the black plague (or some variant of) is always present after the first epidemic. What happens is the local population becomes immune to it preventing it from spreading. Similarly while it is suppressed by that immunity it is learning how to counter it, until finally it does in which case the new and improved form spreads again.
To be even more clear, it never became weaker. From what I've seen the mortality ratings of the Asian, African, and European variants never seem to cull more than 25% of the population. That is until the Spanish Conquests of the New World. The native Americans had never once before been exposed to the disease so it's no wonder that it and other experienced diseases managed to rack up death tolls estimated as high as 90% of the indigenous. Now to be fair it is not definitive whether it was bubonic plague, and or smallpox and or some other pathogen that led to such a number or what the exact number really was. Do bare in mind that an entire empires (that spanned many modern day countries) fall coincides with the Spanish Conquests with Spanish suffering nowhere near the same percent in casualties.