The court upheld decisions of the Supreme Court of Nauru, where the asylum seekers have been exiled since 2013.
A Pakistani man from Peshawar told the court he feared being persecuted by the Taliban if he returned to the Pakistan city.
The court found while there was a real possibility he would be harmed in Peshawar, he could move elsewhere in Pakistan.
Another Pakistani feared he would be harmed by a militant political party in Karachi because he had injured one of its senior members.
The court found he could live in Pakistan's Punjab province, where the party had no power.
The third man was a leader of a pro-monarchy group from Pakhu in Nepal who said local a Maoist group had burnt his house down.
The court found the persecution was not condoned by the state, so the man could relocate within his country to avoid it.
The three men are among the last to bring their legal challenges to Australia which no longer has oversight of Nauru's court rulings.
In March, Nauru ended a 1976 agreement that had made Australia the destination for Nauru's legal appeals.
Rights groups have been critical of Nauru's decision to severe its legal ties with its former colonial master.
They argue Nauru was attempting to avoid outside scrutiny by depriving its own 10,000 citizens as well as the asylum seekers of the appeal option.
Australia refuses to resettle refugees who attempt to reach its shores by boat. It pays Nauru and Papua New Guinea to keep them in detention centres that have been widely criticized by rights groups.