There's a recent development in the Lindsay Baum disappearance that nicely illustrates how much LE knows and doesn't tell. On the Lindsay Baum thread, there are now posts of images from a search warrant for someone's storage locker and car. The warrants are detailed and include quotations from various interviews with a number of people, including the person who is the subject of the warrant. It is hard not to be struck by the painstaking care that LE has taken trying to solve Lindsay's disappearance, which happened in a very small town and more or less out in the open. When we get in a hurry--because we worry that Kyron is out there or because we are human (and in our case, humans prone to sleuthing) and want to KNOW--LE is doing the slow and painful task of talking to people, looking for information, for conflicting stories, for changing stories, for outright lies, etc. Lindsay's case appears to be particularly difficult because it looks like it may be a stranger abduction, which is harder than a case involving family or neighbors.
We see TV shows like Without a Trace that have the FBI or local LE powering through a case in less than 24 hours and we want every case to look like that. And sometimes it does, and a child is brought home alive or the body is found quickly. Most cases, though, involve a lot of slow slogging and digging, a lot of boots on the ground and time. What looks like a lack of urgency to liz b, above, I think, is just the reality of police work. Kyron has been missing for weeks. Once the first 2 or 3 days have passed, the odds are that the child is not alive--or so we think, because we only have a handful of cases in which we KNOW the perpetrator has kept the child or hidden him or her, because if the perp does it successfully, we never know. Shaun Hornbeck, Jaycee Dugard, Elizabeth Smart. There are probably others out there, as well. There is really nothing LE can do to hurry up the process. At least in this case, as in Lindsay Baum's, LE has not given up.
I think LE has an operating theory about whether Kyron is alive (and likely to stay that way because TH stashed him) or not. I think they have a fairly clear picture of the events of the morning at school and an idea where TH's story doesn't hold up, because of the polygraph. I think they have a mountain of testimony from witnesses, the best of which is now known also to the Grand Jury. I think they know a lot about TH's background, and perhaps a lot about whom she has been talking to on the phone or via email for the past several years.