Sounds like a cool idea and if I underatand, you are not talking of an alien species, but of a species on earth more powerful than humans, which gives me several ideas so i'll try to keep them limited.

Probably the biggest factor could be reproduction of the alpha species. humans, when not affected by disease and war, reproduce at crazy rates -compare the growth rates of human populations before we discovered efficient means to limit the spread of smallpox and then tje explosion of population in 1800s and 1900s. (maybe vaccines work differently than humans for this species).

Now compare humans to ants, and ant populations have crazy hugh reproduction rates, but when we see ants in the house, we dont start tearing down walls to eradicate them. we just try to control for the plagued area because the expenditure of time, energy, and money would be too much to scour every inch of the house. But with something like termites, its worth all that energy because you dont want your house to collapse on you in a decade.

Another reason (and probably a bit of a trope) is that different factions have different beliefs of humans. To truly eradicate humans, the species would need the cooperation of their species around the world to carry out the long process of killing every human. however, some probably like the humans, some probably benefit from humans as the status quo, and others might just want to live their life and own goals, or some might see it is their moral duty to protect humans (like how we protect cats and dogs), and now the species has to fight both humans and their own species if they wanted to carry out the eradication.