No it doesn't despawn. If an npc charms your pet, he keeps it until you kill it.
That mages pet stayed for the next people to make an attempt.
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Eberron 60 Erudite Enchanter <Awakenend>
Enjamin 60 Erudite Cleric <Awakenend>
Yxarus 60 Iksar Warrior <Awakened>
Fauvana 54 Erudite Necromancer
Seliel 24 Erudite Rogue
Deepwalter 6 Erudite Paladin
Fauvano 40 Dark Elf Necromancer
Stoppinswords 11 Dark Elf Warrior
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