I don't think that robots will make things worse.
The idea is that even if the 1% own all the means of production they won't just sit there and let the 99% starve.
They expect top class service and goods, and for this they need highly skilled people. And these people don't come cheap, they need education, enough comfort to concentrate on their assigned task rather than in survival and a good pay to keep them working for you instead of your competitor. They will become the 5%.
Now the 5% also want their little comfort too. They won't be able to get top class service like the 1% but they can still get moderately skilled people to work for them, which, in turn, can create work for the lower skill people, and so on...
You'll end up with a pyramid, exactly like we have now, and like we had in the past. The jobs will change, but the idea is still the same.