I have the same general issue, but with slightly different behavior. I print over a network to two different HP laserjets using IP printing. I find I can print just fine from most applications (e.g., Word, PowerPoint) except Adobe applications. When I try to print from Illustrator or Acrobat, the job is sent to the printer and I can see it in the queue. But, as you describe, the printer immediately pauses. If I go into the queue and unpause the printer, then the job immediately stops (the printer doesn't pause, the job stops). If I restart the job, the printer immediately pauses again. It goes back and forth like this forever. This happens on one of the printers I typically use. On the other HP printer I commonly use, the job never pauses, but I get a message in the printer dialog that says: "unable to get printer status (Not Implemented)" On this printer the job is listed as printing, but it never goes anywhere. I have deleted this printer and re-added it, all to no avail.
Note that this happens regardless of whether I use CS3 or an old copy of CS1 that printed fine before I upgraded to Leopard.
I looked on Adobe's web site for a discussion of this issue and found none.