Q: HP 8600 issues

Sometimes it is necessary to delete the printer in System Preferences > Print & Scan, then add it again. Try that.

Mac OS X v10.6: How to connect a wireless-capable printer to your AirPort network: http://support.apple.com/kb/HT3500

Ignore the reference to OS X 10.6. Lion works the same way.

Mac 101: Printing (OS X Lion): http://support.apple.com/kb/HT4670

After Several different approaches, I ended up removing the printer from preferences, powering down printer, powering down computer, powering down wireless router and main internet box for 60 seconds....powered all back up in reverse order and added the printer back into preferences.  All  appears to be working for the last hour.  We will see