I just wanted to post back to say that the problem has been solved by HP Support. They had me go through a few power on and offs with cable disconnected, but none those steps seemed to make difference. The 4th step did - install new printer firmware. I had done this before, but they apparently released a new one a few days ago that fixed my problem. Here is the procedure:
Download firmware update
1. Open the above web site
2. Click on Download button. File Download window will appear
3. Click on Save and Save this program to disk
4. Download file on to your computer Desktop
NOTE: Many of the full HP all-in-one product software program downloads are very large and will take some time to download.
Double-click on the downloaded file and follow the onscreen instructions to complete the installation.
Now check the functionality.
I've been turning the printer on and off all day, and it connects right away, everytime and stays connected. I hope this helps others with the Pro 8600. Cheers!