I agree with Edie about the purpose of the book. I think it's more enjoyable for them to hear what kids their age were doing as opposed to only what adults were doing.
My kids are enjoying it, so I'm not sure I'll be able to help much, but here are a couple of ideas that might work based on what we're doing at home:
1. Read at the breakfast table or lunch table. You have a captive audience because they're sitting still eating, and they can't complain because their mouths are full. (Plus, you won't go back for seconds because you'll be reading when you're done with your first serving!
2. I usually break up the reading with a few interjections. "Wow! This little girl was only 8 years old, and she was responsible for taking care of the baby, mending her family's clothes, and cooking supper. What do you think about that?" Or, "Eeewwwww! Can you imagine having to eat bread that had worms in it?" Anything, really, to help them picture themselves in the character's place. I'll especially try to stop when I feel like there's a little bit of suspense. For example, if the book says she heard a noise, I'll say, "Ooooh, what do you think it was?" It helps them to really put themselves there and imagine what the noise could have been, and then they'll stay tuned in because they want to hear if they're right.
Hope these ideas help. I can't speak as to whether it's a big deal to just drop the book because I'm only in Week 4. Maybe a veteran user will chime in on that for you.