I would hope that in case of a gyro failure the computer would stop listening to the gyros, display a warning light on the dashboard, and you'd be able to bring it to a stop based on the same principles that keep a normal bike upright. You might have to dump it on its side when it comes to a stop, but you shouldn't have to spin off.
The dangers of that are roughly similar to a blowout in a normal car, momentary but nearly complete loss of control.
The angular momentum of the wheels is what keeps it upright (laterally). This is different to the Segway which used the motors to control the forward-backward tilt with position input from a gyro (actually an accelerometer)
This isn't an ordinary cycle - it has a pair of reaction wheels running at some fantastic number of RPM below the seat.
"In final production form, the combined force of the pair of gyros will max out at around 1,300 pound-feet, enough to keep the C1 vertical while stopped"
I see, because of reading the above thread about normal bikes I thought I was still in that subthread and I thought you were talking about the ordinary wheels at ordinary wheel speeds. My bad.
[BTW, the article I linked to mentions that the gyroscopic effect is not solely responsible for stability in ordinary bicycles. There is a site of a guy easily riding a bicycle with an opposite turning plate next to the front wheel to cancel out the gyroscopic effect demonstrating this, although I can't find it.