Are you using the Ardupilot firmware? Otherwise, your motor layout might be different.
I learned this the hard way because the motor map for tricopter is different on Ardupilot & PX4 firmwares.
megabotz
I assumed the OP is using either an APM or Pixhawk with Ardu, since that's the motor layout he posted a picture of. I've flown ArduPilot in various aircraft, including multi's, fixed wing and helicopters, since the APM2.5 days. I had a 650mm quad rotor multi that had an ESC go up in smoke in flight flying a Pixhawk v1 with AC3.3.3 and the autopilot successfully kept control of it and landed it from 165 feet altitude with no damage to the quad with the RF motor completely dead. But that doesn't happen every time when you get a motor or ESC failure with a multi.
Going from four motors to eight doesn't increase the chances of it being successful either. What it does is double the chances that you will have an in-flight failure.
Multirotors are the worst case possible to discuss "reliability" and "safety". They don't actually fly. If you drop an airplane, a helicopter, and a multi, all from 200 feet, and all with no power to the motor(s), both the airplane and the helicopter can be landed without damage by a competent pilot. No matter how good the pilot is, all you'll get is an epic crash with a multi.
So poring over multi-rotor configurations trying to reason "reliability" or "safety" is pointless. Tri's are the most efficient but have no chance of recovery with a motor failure. Quads are less efficient than a tri, but are popular because of their low cost and simplicity. Hex's are less efficient than the above but can typically lift more than a quad or tri with shorter flight time. Octo's are the least efficient of all of the above and are typically used for heavy lift, very short flight time applications.
You introduce losses with each ESC, motor and prop. There are tip losses on the prop. The more props, the more tip losses you have, and the more props you have running in "dirty" air from the tip vortices and turbulence in front when the thing is moving. Each additional ESC and motor has electrical losses. The more you add, the more of your battery energy gets converted to heat instead of thrust. When you lose a motor on an octo, due the entire thing being less efficient than say a quad, it has no better chances of recovery than a quad or hex. The props are all operating at less than 50% efficiency due to the close proximity of tip vortices from other props and loss of thrust on one side will cause the flight controller to start throttling motors to maintain control of it. But your normal hover power is now adjusted to a higher level, the remaining motors at 90 degrees to the failed one are operating at continuous elevated power to provide the vertical thrust vector. The motors opposite the failed one are operating at very low power trying to maintain pitch or roll attitude. Since the small ESC's typically used on octo's are not designed to operate at elevated power for more than about 15 seconds, you are now in danger of burning out another one. And that's usually what happens with octo's is the domino effect of losing one ESC, and then a second one being overloaded, and the thing crashes within 15-20 seconds of losing the first motor.
There are instances where, just like my quad that had a motor quit, the flight controller can bring it in safely. But it just doesn't happen that often.