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There's nothing wrong with an unrealistic premise, as lots of fun books hinge on them and manage to make their story a lot of fun. It's how the premise is handled that changes everything.
For one, a good deal of skepticism would help tremendously and better ground the story in reality. In My Teacher Is An Alien, Susan had to convince Peter to come with her, as he didn't really believe her story, even though he didn't think she'd lie to him. In How a Weirdo and a Ghost Can Change Your Entire Life, Teddy's attempts to convince Martha that he really could communicate with ghosts only made her angry at him until she eventually tried it out herself out of boredom.
Here, Julia tells her friends Lori and Jeff about what happened, and while they think "huh, I don't remember disappearing", they agree to help her solve the mystery and even get excited about it. Though Julia later manages to find more definite proof that something strange happened, they believe her from the start. I think they should have only believed her after she gave them the more definite proof, and even then remained skeptical.
Next up, we have convenient coincidences for the sake of plot. Next door to the school is a military base, in the form of a bland gray building with barbed wire fences. Military security consists of passwords that guards casually say out loud to each other in conversation, and guards who are distracted easily by idle conversation. How could any ten-year-old hope to break in?
Things get a lot more interesting once she's inside and discovers the cause of all the troubles. In fact, the scene with Julia stuck in the wall is one of the most unique scenes I'd ever read in a work of fiction, and the remainder of the book, while still not plausible, is quite entertaining.
It's actually a fun story if you turn off your brain. Part of the problem is its presumed target audience might easily recognize multiple reasons why the story just wouldn't work, fun as it is when it really gets going. Adding a bit more believability in the form of skepticism from Julia's friends, and a more intelligent way of breaking into the military offices, would be a start, but having the top secret project literally be built next door to the school - while vital to the plot - probably tossed all plausibility out the window from the start.
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