Setting a static IP is great advice if your printer is setup on the wireless network. One thing I would like to add, if just uninstalling and re-installing your software fixes your error with HP Solution Center, then you will have no need to go through the scrup techniques and the level 4 uninstall you provided. That step is mostly for registry problems. If you uninstall/re-install enough times, you will get registry problems and have to do that step when the re-install doesn't fix it.
Setting a static IP will allow you to keep communication between your software and the printer if you periodically get this error message. Let me know if I can assist you with this task as I am happy to help, especially if it is only connected via USB.