It was documented on Victory Road that when both or all three of your Pokémon faint that you cannot select another Pokémon, this isn't true however.
(I haven't had all three Pokémon faint in a Triple Battle yet only two
)
Actually when you have all Pokémon faint, select the Pokémon then randomly tap the other five areas, (I had the most luck hitting fainted Pokémon though) this will select your third choice and then select your fourth choice. As I stated above, I don't know about when you have all three Pokémon faint or what it does, But I believe the concept is the same.
So actually this programming error here has it's "fix" as well.