Pythia, welcome to WebSleuths!
IIRC they said they are going to search as long as it takes. They were thinking it was going to take a couple months(?), but I don't remember hearing any end date they had in mind.
It's been awhile could you refresh my mind on the random attempted kidnappings in the area? The only one I'm remembering is the one that the "POI" mentioned as the cause of Jhessye's disappearance.
How far does one need to reach to believe that a random stranger came and found little Jhessye severely beaten, starved and abused, stashed in her mother's closet and then this stranger smuggled Jhessye out of the house in broad daylight, completely unseen by all?
Odder still is Jerice coming home, finding her darling daughter missing, then cleaning up after the kidnapper with bleach, removing all possible evidence that this random stranger had ever been in her house!!
Your post lays it out very well.
LE knows who did it. They aren't searching the landfill because Jhessye was abducted by some random stranger.