I have an H-P officejet d135. If it isn’t used for awhile, it goes into a power save mode. The problem with that is when I want to print something I have to hit a few buttons to wake it up. In addition, occasionaly because of that mode, it fails to be recognized and I have to unplug the USP cable to reset it.
According to p.20 of the (PDF format) manual, the 7:Status and Maintenance menu contains the option 6:Set Power Save Mode Time. I don’t know whether this will allow you to disable it completely, but maybe you can extend the interval so that it isn’t so inconvenient.
HP also has a mostly unhelpful support page on USB connectivity issues.