Inconsistency about the girls in "Prisoners"?

I don't think that there's any inconsistency in the fact that the girls were not killed immediately. The two other victims that we are aware of, namely Alex and Bob (Taylor), were also not killed. Bob Taylor escaped from the Joneses after three weeks (?) of captivity. So it seems that the modus operandi does not involve killing the children immediately.

However, if we assume that Alex was a special case and that Bob was a standard example of how the other abductees were treated, then the question of why they were allowed to live for a certain period of time before being killed remains to be answered. There is no clear answer given in the script. But here is a theory:

The Joneses were unhinged serial killers. But they were previously a very religious couple and perhaps some of that still lingered as they indulged in ritual before they killed each of their victims. While both of them wanted their revenge on god, Holly appeared to be a remorseless but practical vamp. But her husband was more complicated.

Firstly, there was Mr. Isaac Jones' fascination with with FBI agent's book, Finding the Invisible Man, which was about finding a hypothetical kidnapper of children and bringing him to justice. But to Mr. Jones, it was also about finding the other Invisible Man (the one in the sky) and bringing him to justice for killing (kidnapping) his child. Perhaps he/they were daring/beseeching the Invisible Man to rescue the child.

Secondly, there is the maze motif which Mr. Jones is obsessed with. It is also from the same book and is unsolvable. But the drugged children were asked to solve it in order to be allowed to go home. This might not have been an empty promise as it would have essentially taken a miracle to solve it. Perhaps the victims were being given sufficient time to solve the maze before they were killed.

Lastly, there was his confession to the (child molesting) priest. While the priest states that Mr. Jones bragged about his deeds, to me, this could also have been an indirect plea for someone to stop him or an attempt to absolve himself of his guilt. The priest implies that it was not so much of a confession as a brag, as if Mr. Jones was taunting his god. Couple this with the symbolism of the snakes (which represent sin) that he was fascinated with, and you can piece together a religious motive for his behaviour.

In other words, the ritual and thereby the delay in killing the victims was an elaborately indirect (and perhaps subconscious) attempt to allow someone/god to stop him/them from killing another child. The husband was the source of the ritual and Holly continued in the same vein after his disappearance.

I don't think it's inconsistent at all, because these were the first children the woman had taken on her own. She began the pattern of child snatching with her husband who is long gone, and she mentions that she slowed down once he disappeared. Also, these girls weren't the only ones to be kept alive as there's also Alex. She also says she brought them inside because it was lonely without Alex. There was also another kid who managed to escape who is now in the film as an adult. I think you're taking the words way too literally. Just because she says the ultimate objective was to kill children, doesn't mean they didn't also get a perverse kick out of having them alive for a while.

I think that it is consistent. Holly Jones says, "Making children disappear is the war we wage with God. Makes people lose their faith. Turns them into demons, like you." Its easy to understand the parents losing faith because we see it, but what we don't see is the childrens experience during the kidnapping. I believe they kept the children alive to destroy their faith before killing them thus furthering their revenge on God.

I do not think that there is a plausible explanation. The flashbacks Joy has in the hospital show a book with a note 'Solve the maze and you can go home' which immediately makes viewers believe that maybe they were kidnapped by a serial killer who likes mazes and likes to play games with his/her victims like Jigsaw in Saw. I think this was just to thicken the plot. To let them live and keep the viewer guessing about the kidnapper.