[Andrew Hackard]

Padzahr would block the level loss for its player only.

Karkadann Horn can't reverse Padzahr because preventing something from happening isn't a reversible effect as described on the Karkadann Horn card. ("Oh yeah? Well I double UNprevent your prevent!")

Finally, your question has two misconceptions about Divine Intervention. DI isn't a one-shot as defined in the rules, and DI can't be held to play later: it must be played IMMEDIATELY when it turns up.