Australian Daniel Ricciardo managed just 28 laps at the Sakhir circuit before the team decided to suspend running to prepare the car for the final day of the second pre-season test on Saturday.
Red Bull, winners of the last four drivers' and constructors' titles with Sebastian Vettel, have struggled to get their Renault-powered car running reliably while Mercedes and Ferrari-powered rivals have been getting in the laps.
Vettel did 59 laps on Thursday, more than twice as many as the team had managed in all five previous days of testing in Spain and Bahrain, but the gremlins returned for his new Australian team mate.
Ricciardo did his best to sound positive, however, and said the car was definitely making progress.
"It's coming together bit by bit. We'd love a big chunk all at once but obviously that's not the way these things work, so we have to be a bit patient for now," he said.
The team's race engineering co-ordinator Andy Damerum said the mechanics had their work cut out and explained that the mechanical issue was not one the team had experienced previously.
"Because of its nature it means we have to take the car apart," he added.
"These issues are of course frustrating but this was unrelated to the others so it's just a case of tackling each issue as it appears. A tough night in prospect but we hope to get a good day in tomorrow," he said.
While Red Bull struggled, Mercedes powered on with Britain's 2008 world champion Lewis Hamilton fastest and putting in 67 laps.
Compatriot Jenson Button did more laps than anyone, 103 in his Mercedes-powered McLaren, and was second fastest.
Swedish rookie Marcus Ericsson managed the most laps in a Renault-engined car, with 98 for Caterham. The distance covered meant he had done more than the 300km required to gain the mandatory super licence to race.
The season starts in Australia on March 16.
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