After reigning champion Sebastian Vettel completed just 11 laps across two days in the new RB10, the team's new recruit Daniel Ricciardo did not emerge for almost three hours on Thursday and then broke down seven corners into his first lap.
Red Bull's troubles - Gary Anderson's analysis
There was at least some respite in the fact he reappeared in the final minutes of the morning, completing a brief two-lap stint.
That still left the team trailing its major rivals, as Ferrari, McLaren and Mercedes all neared half-centuries in the lapchart.
Of the trio, Ferrari's morning was the most interrupted.
Fernando Alonso - taking over from returnee Kimi Raikkonen for days two and three - caused the day's first red flag when he came to a halt just before the final chicane.
The Spaniard was able to return however and finished the morning second on the timesheets and with 32 laps in the F14 T under his belt.
Button managed 40 in total, and set the outright pace with a 1m25.030s - just under one second slower than his day two benchmark.
Mercedes meanwhile continued where it left off on Wednesday, as Lewis Hamilton clocked 45 laps - which included one 18-lap stint only curtailed by the Red Bull stoppage.
The Briton ended the morning third overall, less than one second off his former McLaren team-mate.
The trio locked out fourth, fifth and sixth, with Massa leading the way and Sutil just edging out Hulkenberg, who only managed six laps in total.
Jean-Eric Vergne was next up for Toro Rosso, his 22 laps a welcome lift for a team that failed to emerge for even a single run on day two.
Caterham meanwhile handed duties to its third driver Robin Frijns, who completed eight laps - none of them timed - over the morning.
The team also had to twice recover the Dutchman from the pitlane entry, where the CT05 had stalled.
With Marussia still working on its 2014 challenger, which is yet to be unveiled, Ricciardo propped up the morning order.