Hello mshuttle-
First let me ask if you are using the wireless function of this printer (ie. connected USB ??). If you are not , then turn the wireless off. If you are connected wireless, this can happen for a couple reasons. The printer needs to be plugged directly into a wall outlet , as the printer has a built in surge protector . Secondly, if you have many wireless devices or there are many wireless networks around you the printer can get mixed signals and not try and "wake" up. If i am correct , this is a 4620 Officejet ?? You can also update the printer firmware at this link : http://h10025.www1.hp.com/ewfrf/wc/softwareDownloadIndex?softwareitem=mp-104396-2&cc=us&dlc=en&lc=en&os=4063&product=5191646&sw_lang=.
I hope this helps.