As a result, Hubble remains in safe mode.
Before the last week, two of the old-design gyros had failed.
The current fault had been anticipated because the gyroscope had been "exhibiting end-of-life behavior for approximately a year", according to NASA.
NASA said if they are unable to recover the malfunctioning gyro Hubble will resume science operations using just one device.
Scientists are now performing analyses and tests to determine what options are available to recover the gyro to operational performance.
The agency, though, said it didn't expect Hubble to cease operations any time soon, as its instruments and other key components are working normally. The space agency says it will update on the matter in the future, but no timeframe was provided.
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Hubble has carried a total of six gyroscopes - three standard and three enhanced - since astronauts installed them during a spacewalk in 2009, typically using three at once. Still, the telescope can function with just two gyros, and it could even continue observing the universe with just one.
The Space Telescope Science Institute's deputy mission head, Dr. Rachel Osten, said the first move "is to try to bring back the last gyro, which had been off, and is being problematic". "The remaining three gyros available for use are technically enhanced and therefore expected to have significantly longer operational lives".
Two of those enhanced gyros are now running. That extended lifetime is something the astronomical community "wants desperately", she added. NASA said that, while this option offers less sky coverage at any particular time, there is relatively limited impact on Hubble's overall scientific capabilities.
Gyroscopes are needed to keep Hubble pointed in the right direction during observations. The current problem, though, is a reminder that, with the retirement of the shuttle, NASA now lacks a means to fix or upgrade Hubble. "Hubble's instruments still are fully operational and are expected to produce excellent science for years to come".