I believe you are editing an object in a PDF, using illustrator. The best option is to edit the original object, then export to a new PDF from the native file, however editing PDFs is becoming more common and necessary. One reason your image could be jumping relates to the way the .ai or .eps was placed. InDesign will allow you to specify media size, bleed size, or image size when placing an .ai file, (or something like that), when you re-save the file, this offset is changing. Prehaps the original file was an .eps and you are saving it as a .ai? Possibly you are adding or enlarging an element in your .ai file, which would also cause it to move- if it had been placed using "image size". If this is the case, you can use PitStop (an expensive Acrobat plug-in) to move it, or save the .ai file as a separate file and place your original PDF and the new .ai file into a new InDesign file and re-export.

This is really an Acrobat question, but here is some additional info- The object you are editing is placed in the PDF at a specific offset, when you add crop marks to it, the offset changes. If you add other elements, or move anything on the edited file, this may also cause the offset to change, depending on how the item was originally placed (by art, trim, bleed, media). Editing an .eps and saving as an .ai could also cause the offset to change, and vice versa.

I feel your pain. You should be able to save a file in Illustrator without crop marks, perhaps someone else will remember where to turn this off and chime in. What versions and platform are you using? Is everything up to date?

One sure fire work-around is to save the .ai file as a separate file and place your original PDF (with the object deleted) and the new .ai file into a new InDesign file and re-export to PDF.

Does this happen every time you edit an object in Acrobat using Illustrator? Are you using Acrobat X and Illustrator CS6? When you open the PDF in Acrobat, go to File> Properties> description, What program created the PDF?

In Illustrator CS3, with nothing selected, you can go to Object> Crop Area> Release. As a diagnostic tool, try this: Go to Acrobat preferences> Touchup> Choose Page/Object editor and navigate to Illustrator CS3 in your Application folder. Open the PDF, edit your object, do an Object> Crop area> Release before saving. Does this fix the jumping issue? Unfortunately I don't know how you can do this in CS4 and above.

You could also try this (I give it a one in a hundred chance of working, but who knows) In Acrobat go to Tools> Print Production> Preflight> PDF/X compliance (convert to PDF/X-3), the idea is the PDF/X-3 specifications might not allow the object (probably some flavor of .eps) to have invisible crop marks and will remove them.

Your Illustrator preferences might be corrupt, but I think this is unlikely.

What happens if you try to re-edit the object (after it has jumped) and select and delete the crop marks? Do they re-appear?

Thanks for posting your fix, that will help other people who might be searching for a solution. When you do a save-as, you overwrite lots of history and "overhead" from the old file, which probably removed the crop marks, or you are opening an .eps and saving as an .ai. I'm guessing the original file came from Word or Publisher.