Hmm, I have another afterthought about this. Can a chosen wielder of the Keyblade reject the offer of taking up the weapon? Or can the power of wielding a Keyblade be removed or taken from someone? Is there any case about this in the series? With the exception of Data Sora of course, since his original was made of data.
In this case I think it's fair to say that if anyone's heart is weakened in resolve then they lose the ability to wield their keyblade. For example, Riku lost his to Sora, but eventually gained his own. On the idea of relinquishing the ability to use it, the only thing we can say for sure is that someone can refuse to use the keyblade, but if their heart is strong and they have the keyblade, the keyblade will stay with them and the ability to use it, too.
As for Data Sora and his keyblade, I think it boils down to the fact that everything in the KH universe has a heart. For example, Pinocchio has a heart, which is clearly stated in the first Kingdom Hearts, even though he is just a puppet. As do worlds. Basically, any living shell will grow a heart if given enough time and exposure to other hearts (my interpretation from Nomura's words). So, whose to say that data taken from a real heart cannot grow a heart in time. Since Sora is the center of the journal, the heart of the data would be the Data Sora's heart. And as we know from Coded, Data Sora interacts with beings who possess hearts i.e. Micky, Goofy, and Donald. The factors are there, so if we go along with my conclusion then it's fair to say that if the real Sora's heart is capable of wielding a keyblade then so should Data Sora once he grows a heart.
On to Ansem's/Xemnas's keyblade fiasco. The cutscene where Riku is talking to Ansem Seeker of Darkness, or Xehanort's Heartless, he says that because Ansem had let his heart go into darkness, he lost the use of the keyblade. That is entirely wrong. There are keyblade wielders of light and darkness. Master Xehanort clearly had darkness in his heart, and yet he was one of the best keyblade wielders in the entire series. You could argue that he was just manipulating the darkness, and that he never had darkness in his heart. And I could say that at the end of KH3 Sora is going to kiss Kairi in a big emotional scene. Point is, we don't know the state of Xehanort's heart. Based off what we have, darkness doesn't make one lose their keyblade. I think the reason Ansem SoD can't use his(don't know if I should be saying his here) keyblade is because he is a heartless. It wouldn't make sense for a heartless to be able to use a keyblade, whether or not that heartless was made from a keyblade wielder. Nobodies apparently are capable of wielding keyblades, as seen by Roxas, and so it stands to reason that Xemnas should be able to wield one too. BUT (this is a very big but), it is apparent that when Master Xehanort was defeated by Terra's Lingering Will, and then subsequently lost to Aqua and fell into darkness, he lost most, if not all of his memories, save for the name Xehanort. That means he had lost his memory of the keyblade. Now I know what you're thinking: "In DDD, the scene where Terranort murders the apprentices and Lea and Isa showed him wielding a keyblade! Explain that!" And I say to that: I DON'T KNOW! Nomura really has got A LOT of explaining to do in KH3, and I hope that he addresses this. The best explanation that I can offer is that Xehanort's heart took over Terra's body in that moment and when it did, he could use the keyblade. This entire topic leads into a whole different theory I have about Xemnas and Ansem SoD, particularly about their split from Terranort, but that can wait for another time.