How do I create a PDF that has gradients in it that can be edited in Illustrator?

We have Enfocus Pitstop for direct PDF editing as well as a few other tools but these are all very cumbersome and lack 90% of all features Illustrator offers. My job is checking artwork we receive, fixing it where needed and making alterations to the design. Using those tools makes my job take 5 times longer and 10 times as frustrating IF the tools even offer what I need them to (and often they don't).

At least half the time we only receive a PDF file - the previous printer usually doesn't want to send their open files but like I said, normally this is not a problem - the myth that Illustrator cannot reliably open PDF files is just that: a myth. EXCEPT when it comes to InDesign's gradients. Considering this is from the same company, it goes to show how apathic Adobe is to making their teams work nicely together.

The fact that InDesign & Illustrator, two programs that are closely tied together (in fact Illustrator received most of InDesign's unique features over the past ten years making InDesign even more obsolute for most users), can still differ so wildly in user interface, shortcuts, behaviour, approaches, etc. is beyond me. InDesign to me feels like a sluggish awkward beast. It's as if the designers refuse to move on from the old Zeitgeist of the days of Quark Express where the program HAD to be a pig to work with or it didn't feel professional enough.

Hi Barb,
Not quite the solution I was after, so I'll just reiterate my issue.

I've saved a PDF from InDesign. I open it in Illustrator. When I look at the artwork, the part that contains gradients loads as empty, whilst the rest of the artwork is as you'd expect.

Attached shows the problem

ta