What version of designer and acrobat/reader are you using? I tried later versions (8 and 9) and it paged correctly when all the parent containers where set to flow, all page-break and the fields set to auto-fit. If i remember correctly there was a bug that a single growable text field could not span multiple pages. not sure if that was in 6 or 7.
I keep looking at
Forms > Add - Edit Fields
but cannot locate a control for setting the text to "flow"
the Properties just have
General / Appearance / Options / Actions / Format / Validate / Calculate
or for setting the Layout to Allow Multiple Lines
Ah ok, you are probably not in the right forum then. This one is for XFA-based forms built with Designer (accessed through Forms->Start Form Wizard, Create a PDF Form from scratch) and not the in-built Acrobat Form->Add Or Edit Fields. I dont think the in-built fields have the funtionality you are looking for but you can ask in http://forums.adobe.com/community/acrobat/forms