While I agree Bagpuss' dm is well....wrong, guys let's try to be a bit more positive in helping BP, give some more rules quotes and ways to convince the DM he is wrong.
Seriously, it's a problem I actually recently considered, when designing a monster with a condition that ends on its next turn. Dwelling briefly on the hilarity of ruling like Bagpuss' DM did, I ended up ruling that the monster's initiative card stays in the stack until all such conditions have ended. They thus last as long as they normally would - I found it weird if they got cut short just because the monster died prematurely. Of course, one could rule they would in fact get cut short, if we're talking about spell-like abilities or some such.