Interesting - thanks.
I hadn't really considered the definition of asexually reproducing species - it seems that things are much more clear cut for ones that sexually reproduce since then we can use the more clear cut "point of no return" definition.
I suppose in cases like beefalos and mules, or these ring species, this "point of no return" comes down to is there any path for to the DNA of these divergent animals to recombine, so a fertile female beefalo (or the occasional fertile female mule) still provides that chance.
It seems that in general it's rare for widely divergent animals like zebras and horses to interbreed in the wild, but apparently western wolf-coyote hybrids are not that uncommon, so it's more than just a theoretical possibility. Who knows, maybe global warming will force polar bears to adapt to warmer climates and increasingly interbreed with grizzlies.
Even in the cases of species that roughly meet the naive high school definition, it is at least sometimes the case that they can still interbreed, they just don't. Usually, this is because of geographic isolation. Take African and Indian elephants, for instance. They diverged long enough ago that they're morphologically distinct, not just genetically distinct, but they can still interbreed. They don't because they live on different continents, and they probably wouldn't if they were put together outside of captivity because they're intelligent, social animals with culture and learned histories who rely on not entirely biological cues regarding who to breed with, just as much as humans do.
In reality, we first categorized life into species because they either looked different or we found them exclusively in different places, and only centuries later did we attempt to figure out exactly why and how this was the case and reverse engineer some sensible definition onto the pre-existing categories, but it turns out there is no single definition that works universally and has zero exceptions. It's frustrating if you're a language pedant who likes clarity, but a lot of categories and definitions are like this.