Suspended Greek sprinters Kostas Kenteris and Katerina Thanou might have to wait until 2006 for a decision on their futures.
Kenteris and Thanou were alleged to have missed three tests
The duo appeared before the Court of Arbitration for Sport in Lausanne, Switzerland, on Friday and Saturday.
But there was insufficient time for all the witnesses, including Thanou, to testify, so another CAS hearing will be needed to decide the case.
The IAAF is seeking to ban the duo for allegedly missing three drugs tests.
Kenteris and Thanou were provisionally suspended by athletics' governing body, the IAAF, last year but the decision was subsequently overturned by an independent Greek tribunal.
The IAAF then appealed to CAS, which will have the final say on the matter.
The CAS hearing into the case lasted for 12 hours on both Friday and Saturday.
Kenteris testified for seven hours on Saturday and did not leave CAS until 2000 BST.
Kenteris and Thanou have been unable to compete since the IAAF's action against them.
They withdrew from the 2004 Olympics after allegedly missing a test at the Olympic Village on 12 August.
They then spent four days in hospital, claiming to have been injured in a motorcycle crash.
It was the International Olympic Committee's demand that the IAAF investigate the affair that led to the hearing of the Greek tribunal.
The sprinters face separate criminal charges in Greece for the motorcycle crash and for allegedly avoiding the tests.
Their coach at the time has been banned by the independent Greek tribunal for four years for his involvement in the case.