Barbara King lays out necessary conditions: 1) that "individuals of the same species choose to stay together in contexts that go beyond survival and reproduction" and 2) emotional "suffering results when the relationship between the two animals is severed for some reason." Her fears about applying those rules:
For one thing, using these criteria, love will be defined too often only in retrospect, once the relationship is over. For another, it's doubtful whether these criteria could distinguish between love and friendship. (Or, maybe, genuine friendship always encompasses love?) For a third, animals in the wild may ill afford giving off visible signs of weakness, so emotional suffering may be felt but hidden from view.