To guarantee it'll never run away, you need to either keep it on its leash (or unleash it, but put it back on as soon as the 24 hour cooldown expires), or get Natalie to tame it for you. The former can be purchased after taming it by being a bimbo, while the latter costs a bag of silicone and requires that Uveto's been unlocked (as that's where Natalie can be found).