Hello helpinCT,
Welcome to the HP Forums! I hope you enjoy your experience here.
I understand your Officejet 8600 keeps stating offline. I will do my best to assist you! Please follow this entire HP document on Printer Does Not Maintain Wireless Connection. Try assigning a "Static IP Address", which is indicated from this document.
If this doesn't resolve your issue, then please follow this HP document on 'Printer is offline' Message Displays on the Computer and the Printer Will Not Print.
Please post your results, as I will be looking forward to hearing from you. Have a great day! :smileyhappy: