Helly GaryMats,
Welcome to the HP Forums.
I understand that you're having an issue with the icon from your Officejet 8600 disappearing from the desktop. I will do my best to assist you with this.
To start I have some questions for you:
1) What is the operating system of your computer?
*Mac - OS X: Finding your OS version and build information.
*Windows - Which Windows operating system am I running?
2) Did you upgrade from a previous version of the operating system to a newer version?
3) If it's a Windows PC, when the icon disappears off the desktop is it still in Devices/Printers?
4) What type of firewall/anti virus security is on the computer?
5) If it's a Windows PC, do you have an automatic back up software programs? (example: Carbonite, Dellbackup, ect..)
6) If it's a Windows PC, have you run any clean up utilities on your computer? ( CCcleaner, PCdoctor, ect..)
Generally from my expirence, this tends to be caused by some of what I've asked about above. Something not working correctly on the computer, seeing the program as something that shouldn't be there.
I will look further into this for you though, and look forward to your reply.
Thank you for posting on the HP Forums.