when do feral animals that have a stable population in the wild be considered wild and not feral?

Unless a feral population has evolved into a new species (i.e. reproductively isolated from its parental species), it is considered the same species.  The dingo, for example, is a feral domestic dog that has reverted to a life independent of humans, but it is still considered either a subspecies of the domestic dog or a subspecies of the gray wolf, depending on the taxonomist.

If the species did not originate in that ecosystem, it is always considered feral.  The wild boar population in the US is not truly considered wild.  The only native porcine in the US is the peccary.  All "wild" boars are feral pigs.  Some maybe 2 generations old, others may be 500 generations.  Since new feral pigs are constantly being added to the existing feral population, its difficult to establish a singular genetic identity to the pigs.


It's the same with the rock dove/ domestic pigeon populations.  The oldest birds have been around since the 1500s, and have reverted to the wildtype plumage of the ancestral form and some people call these old form looking birds rock doves.  However, new domestic pigeons are constantly being added.

Any population of animals introduced by people, be it 400 years ago, or just 5 weeks ago is called feral.  Dingos are ancient feral dogs, but they are feral dogs all the same.  The oldest, relatively stable population of feral dogs is the New Guinea Singing Dog.  However, its still considered a feral dog.

Perhaps another way to put it is:  wild means native or endemic to the area, feral means formerly domestic stock, living independent from humans.