I don't see how statues of limitations is connected to the question.
The closest I can think of is a right to a speedy trial, but that has so many exceptions (for example if the person is out on bail) that I couldn't say how a judge would rule in this scenario. Especially if it was the defendant causing the delay by refusing to reveal the password and making the prosecutor get it the hard way. (Not applicable in this case, might be applicable in another.)
The FBI is not doing this for proceedings related evidenciary purposes but instead for investigative purposes. No one has been charged here (from what I know) so the issue of speedy trials is moot while the statue of limitations on the crimes under investigation are likely extremely long if they exist at all.