On many satellites, you need at least 3 gyros to maintain control in all 3 axes. If you have less than that, it might not be possible to maintain even rough control because the satellite might start tumbling in one axis.

On the DSCS-III comsats that I used to control, we had 4 gyros (we called them reaction wheels). They were arranged in such a manner that two of them worked together to control pitch and yawl, and the other two worked together to control roll and yaw. You could lose one gyro and still maintain control, but that wasn't so difficult because you really only had to manage 360 degrees of rotation in pitch per day while maintaining pointing accuracy. If we lost 2 wheels, the backup was to turn on thrusters for attitude control (like they did on SOHO). That was projected to shorten operational life significantly.

According to this source

Prior to the next servicing mission, the model indicates that the reliability of the Hubble gyroscopes dominate overall system reliability. Three gyroscopes are required to perform Hubble science operations. Of the six gyroscopes on board Hubble, four are currently functional (Gyroscopes 1, 2, 4, and 6) and two have failed (Gyroscopes 3 and 5). Given the current service mission launch date of May 5, 2005, the probability of 3 or more functional gyroscopes still available then is approximately 70 percent. However, the probability of 3 functional gyroscopes decreases rapidly for a launch date after May 2005.

From the predictions, the probability of 3 functional gyroscopes is approximately 50 percent as of December 1, 2005, and only 30 percent as of July 1, 2006.

It should be noted that the modeling of gyroscope failure probabilities is statistically stronger than has been possible for other spacecraft components. It is based on the performance histories, both in ground testing and in flight, of over 90 similar gyroscopes across many programs. The gyroscope analysis includes both random failures and physical wear−out.

The Hubble has no propulsion system, so dropping to two gyros would have an impact on operations. This paper discusses a way to operate the Hubble in a 2 gyro mode and still do some science. This is discussed in greater detail here. Beyond that, when you're down to a single gyro, it may not be possible to controll attitude at all.