NCT Controller described a communications failure involving a visual approach clearance; the SFO landing flight crew failing to respond with their 'call sign.'

Narrative

Air Carrier X [was] on base for SFO [Runway] 28L. I turned the aircraft at Air Carrier Y and issued traffic. Air Carrier X reported traffic in sight and I instructed Air Carrier X to maintain visual separation. Air Carrier X replied without call sign. I again told Air Carrier X to maintain visual separation and it responded without call sign. I then issued the airport position; which Air Carrier X reported in sight and I issued a visual approach to [Runway] 28L; 'Follow the A319.' Once again Air Carrier X responded without a call sign. I told Air Carrier X he needed to respond with a call sign and he didn't. He then went a couple of transmissions without answering. I was told by the FLM who had been monitoring the situation to send Air Carrier X around; but Air Carrier X finally answered with a call sign and I issued appropriate instructions and shipped the aircraft to SFO [Tower]. Air Carrier X called and talked to the OMIC. He said the First Officer's headset was malfunctioning; but the crew didn't realize it until they got on the ground and it started doing the same thing it had done on my frequency.