The pilot contacted Cairns Tower at 30 miles DME (Distance Measuring Equipment) inbound on the 153 radial (south-south-east of Cairns), and was subsequently cleared to make a visual approach at 2053 hours. At 2054 hours the pilot was given clearance to land on runway 15, and at 2056 hours he reported that he was making a missed approach because he had lost visual contact with the runway. The aircraft was given instructions to make a standard missed approach, and to intercept the localiser via the 15 DME arc (15 miles north of Cairns) for an ILS (Instrument Landing System) approach. At 2104 hours the pilot reported that he was "having a little trouble" and would like to go around again and make another approach from the 18 DME arc (18 miles north of Cairns). After subsequently being cleared for final approach on the ILS, the pilot then reported that he was "having trouble with radio aids" and would like to climb to 7000 feet. The aircraft was later cleared for a further instrument approach and landed at 2131 hours. The next day, checks with the company revealed that no aircraft unserviceabilities had been reported by the pilot and that the aerodrome ground radio aids were all functioning normally during the arrival of VH-TAI. No report had been made to the company by the pilot concerning any irregularities during the flight. A readout of the Flight Data Recorder was carried out to ascertain the track and altitude profile of the aircraft during the approaches at Cairns. This revealed certain irregularities including a Ground Proximity Warning "Pull Up" signal which operated for between 6 and 10 seconds at 2055 hours. This device is to warn the pilot when the aircraft is in danger of collision with terrain. The warning is considered to have been genuine as the terrain closure rate at this time was in excess of 6100 feet per minute, and the aircraft was in the vicinity of Earl Hill which is 722 feet above sea level. The weather at the time was overcast but fine at the aerodrome. There were rain showers in the area, and visibility was reduced to 4000 metres in rain showers. The two preceding aircraft had been able to make visual approaches. The crew declined to make themselves available to the investigators for interview, apparently under direction from their industrial association. This action by the crew hampered the investigation and resulted in the causal factors of the occurrence not being determined.