Members of the so called Nauru 19 believe the government is continuing to blacklist them despite their court case being thrown out.
The Nauru 19 were acquitted last month of long standing charges over an anti-government protest.
The judge in the case, Justice Geof Muecke, referred to the blacklist maintained by the government to ensure the group would struggle to get employment and be handicapped in other ways.
One of the Nauru 19, former justice minister, Mathew Batsiua, says these limits are still in place.
He said last week the Health Minister apparently ordered the Director of Health to deny access to the island's de-compression chamber for a member of the group, diver Rutherford Jeremiah.
"There wasn't any clear reason given by the Director but because we have been living under this discriminatory practice of our government for the past three years we have reached a conclusion that it was simply that Rutherford was a member of the Nauru 19.
"So he was being targetted by the Minister not to receive this life saving treatment."
Mathew Batsiua said another member of the Nauru 19, former president Sprent Dabwido, is in Thailand waiting for cancer treatment that the government is yet to authorise, despite clinical approval being given on the island back in April.