Disclaimer: I'm not an attorney. However, my opinion from following other cases here is that they will eventually be arrested if they don't produce the kids. It seems like the process is simply different/slower/more complex here than it is in the UK. As more time passes without anybody having seen the kids to verify that they are in fact alive, the fact of how long it has been alone can become part of the evidence/probable cause for more warrants to be issued.
I don't think it is any coincidence that the child protection order was served on Lori just after 4 months had passed without any confirmed sightings of JJ and Tylee (they were last seen Sept 23 or Sept 24 and the order was served on Jan 25, with additional search warrants served Jan 26). Police have indicated that the children are not in Hawaii and there is no evidence the children were ever with Lori and Chad in HI. They have known about Chad and Lori's location for weeks. But for some reason LE did not serve them with this order or additional search warrants before now. I think there must be some law that the Madison County Prosecutor was able to use that involves that passage of time (4 months). Maybe a homeschooling law or maybe something to do with the social security benefits the children would be receiving due to their fathers being deceased. I don't know what law it could be. But my opinion is that 4 month time mark was used to get the order and the additional warrants. They are very slowly building a case with everything they have gathered. We don't know what evidence they have or what they lack still to prove foul play. Unfortunately, if they don't have evidence of the kids being dead such as their blood in a vehicle or house it can take a lot longer for an arrest.
MOO.