Right now I think he lacks the mental capability to win the Tour. In almost all of his interviews he seems nervous, pressured, tense, uncomfortable and even unhappy. He has lost all of his youthful lightness of heart which was characteristic of him in the early years of his career. I remember him in the Giro 2007: totally relaxed, laughing, joking ... same in the Tours 2008 and 2009.
I think the difference then was that no one really expected him to win. Therefore, he could only do well and positively surprise people. But in 2010 he saw that he could actually win and since then he seems obsessed in an unhealthy way (I suppose you have to be obsessed to win in the first place). Maybe the chaingate incident also hit him harder than he admitted in the press, a velonation feature from January suggested he might have been depressed, which then might have played a part in the Vuelta fiasco.
I am also unsure as to whether the creation of LEOPARD TREK was the right decision in terms of pressure. Instead of only being the leader of a team he now practically is the creator of a "national" team. His brother Fränk doesn't seem to have been affected by the move though, but he has been much more relaxed and laid back for a while now. It's funny because it used to be the other way around: Fränk used to be much more nervous and uncomfortable on the bike than Andy. I think the many years of experience, as well as his wife and daughter, have calmed him down a lot and he now looks much more confident in his riding (Tour de Suisse, Critérium). He even cracks jokes in interviews such as "I started the sprint in seventh position and I finished in seventh" (on Mûr de Bretagne) or "I told myself: ça passe ou ça casse" (Either you make it or you break it).
It seems that both Evans and Basso have a rather large advantage on Andy as far as psychological strength goes. Both have a huge experience and have nothing left to prove: Basso won multiple Giros and came back from a doping ban, Evans won WC and a whole bunch of other races and is on a weak team. They both approach the end of their career - they can't really let anyone down, they can only do well and positively surprise people. As to Contador, he certainly must have the confidence of having won every GT he ever entered, as well as a natural ability to overcome adversity, even within his own team.
However the OP asked whether Andy could "ever" win the Tour, and to that I say yes. Psychological strength and maturity are acquired through the years and I am confident that Andy might develop in the same way as Fränk and calm down at some point. If he will be able to do that, he will be much stronger than he is today.