Does anyone know whether keeping an animal of one sex as a pet is considered Tza'ar Ba'alei Chayim or not, since it cannot mate?
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Tza'ar ba'alei chayim concerns practices that physically or (perhaps) psychologically hurt the animal. Aside from the possible case of a female animal in heat, not mating does not appear to cause distress to animals. Anecdotally, Judaism 101 reports a story of an Orthodox pet owner giving a pet birth-control pills and asserts that this would not be a violation of halacha.
The absence of evidence is not itself necessarily evidence, but I have never heard of anybody with a single pet being required to get another or give up that pet, and I know lots of Jews who have one cat or dog.