Why should the 1% slave to support the 99%? What would be their motivation?
If you have to ask this question, I have to surmise that you're not familiar with a joy of an interesting job well done. Don't worry about it. There are enough people who are willing to work for the sake of doing interesting things and/or killing boredom.
Why would they not join the majority or simply move someplace else where they can keep more of the value created by their labor?
There won't be anywhere where they can keep "more of the value". When you get into the situation where 99% are jobless because of automation, there are only two ways to go from there: either you have wealth redistribution, or you have a Luddite uprising that smashes the machines and rewinds the civilization back, and forces it to stay there to maintain social stability. The former option allows for further technological progress, the latter does not. If you personally had that choice, which one would you take?
On the other claw, it could also create tyrants from that 1% as they could demand compliance or cut off the tap, so to speak.
There's no way to demand compliance when there are literally hundreds of people lined up behind you willing to do the job that you're currently doing.
Like so many socialist style schemes, it requires humans to behave and act counter to basic human nature and without attempting to game the system. History has proven time and again that such schemes only work among a relatively small and culturally/politically homogenous population, and do not scale to multiple hundreds of millions of a culturally/politically diverse population.
History of past economic systems is generally not applicable to newer ones. If you tried to forecast the success of a capitalist system based on your personal experience in a feudal society, and the past historical track record in, say, Antique slave societies, you would have to conclude that it's an unrealistic utopia, because 90% of the population are needed just to grow the food for everyone else.
Thing is, as technology advances, it eventually accumulates enough changes to force a significant leap in how economics work. It's not really voluntary - the society either makes a leap (and this can also go smoothly or bloody, depending), or it falls off the progress bandwagon and gets stuck in past, and eventually gets conquered or otherwise pushed around by those who stayed on the track.
Capitalism is based on the notion of a workforce that has to work for a living, and on there actually being enough work necessary to satisfy the day-to-day demands that everyone has to do their parts. This assumption is not going to hold true for much longer. In fact, it wouldn't hold true in developed countries today already, if not for outsourcing - why bother with robots if Chinese ex-peasants are a dime a dozen? But those peasants will ride capitalism into middle class themselves, and then outsource to Africans; and then Africans will ride it, and then there's no-one to outsource to - and then it's robots anyway.
And just as feudalism couldn't survive and compete once agricultural techniques advanced to the point where the majority of the population didn't have to be involved in it, so capitalism won't survive once industrial production advances to the point where a single human is sufficient to control a factory that can supply the demands of an entire city.