If your page layout is amenable to it, I'd suggest using a single table with 6 cells (or more if you need gaps between the content) rather than 6 frames. If you're going to persist with frames, however, I'd suggest grouping them once they're positioned correctly, so they'll only move as a group.

On a more general note, the positioning of floating objects is always unstable in a document where content ahead of them is subject to editing, because the edits can change where on the page - or even which page - the anchors for those objects are located.

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Cheers,
Paul Edstein
[Fmr MS MVP - Word]