After reading this thread I thought it might be a good idea to re-emphasize a point made by Peter high up in the thread in case you missed it.
Any brochures, flyers, etc. that you may have started from a brochure or flyer template in Pages would have been based on a Page Layout Template, not a Word Processing Template. You would have had none of the troubles you wrote about if you had begun with a Page Layout Template for this recent project. If I were you and wanted to convert my document to 1-Page per Section arrangement, I would be converting to a Page Layout template at the same time. It's tedious to make the conversion, but you will find many benefits to using the right tool.
Workflow to fix the problem I have created for myself....
1) Create a new blank Page Layout document, position it on screen next to my original word processing layout.
2) Copy all graphical elements from first page of problem (WP) document.
3) Paste into new Page layout doc.
4) Lather, Rinse, Repeat for the remaining pages.
Thanks everyone for the feedback.
Download the Pages User Guide from your Pages Help menu. It is a 200 pages pdf. Read at least the first three chapters. Your frustration comes from you think something should work or behave in a certain way and when it doesn't you are "shocked". I found Pages difficult at the beginning as it didn't work as I was used AppleWorks was working, but taking my time with the User Guide and the book The missing manual for iWork i "relearnt".
If all applications worked in the same way we don't need all the applications but one, right?