Gyros spin very fast on very efficient bearings. A rotating mass will not stop immediately unless forced to do so. So even when power fails completely, the gyro

Gyros spin very fast on very efficient bearings. A rotating mass will not stop immediately unless forced to do so. So even when power fails completely, the gyro will continue to rotate for quite some time (several minutes probably) and fulfill it's purpose - well, unless something penetrates the gyro housing and blocks the spinning wheel. But then I guess your problem is not limited to falling over. Another issue with fast spinning disks is that they can rupture and send splinters flying, but it's rather unlikely that both gyros fail in the same catastrophic way at the same time.