In the case of zombys I believe when you get more than 10 all your pets vanish. In the case of mustache golems when you summons one it will often make all your pets vanish or make your slime vanish. The same has the same case as the mustache golem. Pretty sure only supposed to be able to have one mustache golem but it shouldnt case other pets to despawn and the same goes for the smile. I have a feeling other pets behave similarly but have not tested it.