They've been around long enough now for there to be past performance figures you can google for. I think you'll find the results aren't very encouraging.
I personally don't think there's a huge risk that the robots will lose all your money, but there's every reason to expect they aren't likely to perform better than traditional managers or beat the market. At the end of the day the robots are employing a lot of analysis and management techniques that traditional managers have been using, and since traditional managers use computers to do it efficiently there's not much gain IMO. Yes in theory labour is expensive so cutting it out is good, but in practise, in this case, the amount of money being managed is huge and the human cost is pretty insignificant. I personally don't believe that the reduced fees represent the cost of the human management, I think it's just marketing.
There might be some risk that the robots can be 'gamed' but I doubt the potential is very great (your return might in theory be a fraction of a percent less over time because it's going on). The problem here is that the algorithms are functionally broadly known. No doubt every robo adviser has its own algorithms that in theory are the closely guarded secret, but in reality a broad swath of the functional behaviour will be understood by many people in the right circles, and that gives rise to predictability, and if you can predict investment/trading patterns you can make money from those patterns. That means humans making money (taking margin away) from the robots, or robots making money from other robots that are behind the curve. If robo advisers continue to take off I would expect them to under perform more and more.