Another reason that elites often feel like losers is that they are at the very tail end of the bell curve when it comes to whatever skill or talent they are elite at. At the end of the bell curve you have a huge variance between people, in a way that you do not in the middle of the bell curve. So the chances are very good that you are in close proximity/competition to someone who is not just better than you at something you are supposed to be good at, but much, much better/smarter/faster/etc. I experienced this phenomena in college and grad school.
As for what is to be done, the best thing I can think to do is to produce more elite slots by devolving our increasingly consolidated world to more local control. This will produce more elite slots at the cost of some efficiency, but that's probably the right trade off for "loser" elites, as well as for non-elites for whom the elites would become more accessible/more closely aligned.