It seems that the spell Dismissal can not only Unsummon the Houndmaster's Dog, but also kills it. The Rogue Perk from Level 8 Arcane Trickster, can also unsummon the dog (but not kill it) when using the Perk's ability (Spell Thief).
This may have something to do with the dog apparently being considered a summon and not a familiar or companion.
Voicechat for the dog is /v s
Both should be fixed for next reset.
When performing the Sahuagin Quest on Lobliblop the Priestess used a Banishment and that once again killed my Hound.
Even familiar can be unsummoned using banishment. The only thing that I can think of to protect it is having your summon have higher SR then the spell pen of the monster. Then you resist it all day. :)
Would it be easier to just tag them with "Spell Immunity: Banishment"? I don't really know anything about scripting or coding, but is this a good solution?