How to keep bracket lines from moving

Select them and disable autoplace in Inspector

I think the more fundamental problem is that you have added most of these brackets incorrectly. When I click on, the dotted lines show it is attach to entirely different notes than what it is displayed over. It works much better if you attach the bracket to the correct notes, rather than attach it to one set notes then drag it over different ones. So for example, select the notes you want the bracket to cover, then click the symbol in the palette.

That said, it's not clear which brackets you mean or where you want them instea.d In general, you shouldn't need to disable autoplace for this - I moved some of your brackets onto the staff, saved, reloaded, and they were exactly where I put them. However, I see you are still using 3.1, that's over a year old. You might be seeing a bug that was fixed long ago. I think if you update, and also fix your brackets to be over the correct notes, you'll be much happier.