Shakeel Afridi, who ran a fake hepatitis vaccination programme as cover for an operation to find the 9/11 mastermind, was in 2012 found guilty by a tribal court of having ties to militants and jailed for 33 years.
The conviction was widely seen as politically motivated.
Last year a tribunal cut 10 years off his sentence, but he filed an appeal in March seeking bail and a fresh trial.
"Yesterday (Wednesday) the judge again asked for the record and the Khyber administration did not submit it," Qamar Afridi, adding that a new hearing had now been set for October 16.
In his appeal Shakeel Afridi had asked the tribunal to review the entire case and acquit him or grant him bail until it was heard.
"We are of the view that either Khyber administration is using delaying tactics so that Dr Afridi continues to languish in prison or they have lost the record," his lawyer said.
The 2011 killing of Osama Bin Laden caused massive embarrassment for Pakistan and particularly its powerful military, which was accused of deliberately concealing him for possible use as a diplomatic bargaining chip with the US.
Some US lawmakers have said Pakistan's handling of the Afridi case was revenge for assistance in aiding a foreign power, and the US is withholding USD 33 million in planned aid pending Afridi's release.
