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?
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.