If I use Beartic's "Daunt" attack, but then Beartic is KO'd by Poison, does the effect of Daunt reducing damage done by attacks from the Defending Pokemon go away?

No, the effect of Daunt resides on the Defending Pokemon, not on Beartic. However, if the Pokemon that was attacked by Daunt evolves, goes to the Bench, or leaves play then the effect of Daunt goes away.

Relevant cards