Is there something that Padilla knows that makes it imperative to keep him incommunicado? Aside from the legal and constitutional issues, this just doesn't make sense, when compared to the treatment of Reid, Moussaoui and Lindh.
That's possible, and the legal procedures need to address that possibility. Something like the procedures intially used for Moussari (or however it's spelled in the Roman alphabet), where security-cleared lawyers handle the interface between the defendant and the court when sensitive areas are involved, would work.
(Moussari fired his lawyers and decided to defend himself, thus cutting himself off from certain information. Since he voluntarily chose to do so, and was presumably made aware that this was a likely result, I don't see any civil liberties issue there.)