When the trust bought the reserve in 2009, 48 breeding pairs of yellow-eyed penguins called Long Point home.
At the start of this latest breeding season there were 18.
Necropsies performed at Massey University had now confirmed both birds died from wounds consistent with dog attacks.
During a check on moulting penguins at the reserve south of Owaka early this month, trust ranger Ben Goldsworthy discovered the body of the second bird - a ''bloody and recently-killed hoiho'' - with dog tracks nearby.
The trust ''can't afford to lose any more to dog attacks'', he said.
Department of Conservation Murihiku operations manager Tony Preston said dog owners were required by law to ''ensure their dog does not injure, or cause distress to wildlife''.
Early this year a dog killed a Snares crested penguin on the beach near Kakanui.