I have to say I disagree with DisturbedNeo's answer. When you watch the episode, after she zaps herself, The Doctor is handcuffed to a pipe, with no one else there. With Mr. <PERSON> distracted by all the people who suddenly returned, I don't think the first thing he did was run back to see The Doctor and <PERSON>.
Furthermore, before the conversation where he figures out what's in the screwdriver, you see that they're beginning to evacuate the people that were saved. Seeing as though they had no idea that the people were even going to be alive, I doubt very much they had ships ready for them to teleport to (admitted, maybe it's an interplanetary teleportation network, and that's irrelevant). They would presumably have to do a bit of work coordinating things (though I'll admit that CAL might be able to help now that she's able to think clearly), during which time <PERSON> tried to find <PERSON>:
DOCTOR: Any luck?
<PERSON>: There wasn't even anyone called <PERSON> in the library that day. I suppose he could have had a different name out here, but, let's be honest, he wasn't real, was he?
So, to sum up, after <PERSON> zaps herself, the following needed to happen:
* <PERSON> finds The Doctor handcuffed and releases him (presumably after explaining what happened to many confused people)
* <PERSON> tries to find <PERSON> and fails
* The return of all the saved people to their homes begins to get organized
That said, I think part of the explanation can be found in the following quote:
DOCTOR: There's a neural relay in the communicator. Lets you send thought mail. 45
That's it there. Those green lights. Sometimes it can hold an impression of a living consciousness for a short time after death. Like an afterimage.
<PERSON>: My grandfather lasted a day. Kept talking about his shoelaces.
So, we know that some people last longer than others.
Also, given that Ms. <PERSON> was not very bright, perhaps her pattern wasn't as strong to begin with. If that does have something to do with it, then I think <PERSON>, a chosen companion of The Doctor, would be a very strong pattern.
Furthermore, this was a neural relay that The Doctor himself put into the screwdriver. Given his own knowledge of psychic phenomena, technology, brains, and, well, practically everything, I think it's safe to say he might know a few tricks to keep the pattern from degrading as quickly which could incorporate into the design.
Together, I think these factors allowed <PERSON>'s pattern to survive. 417