Same printer, same issue.
Set a Static IP Address- several times (which was a lot of fun because I kept losing the connection while trying to do this)
DIsabled Sleep mode...so far so good, but while waiting to find out, disabled UPnP just in case.
Has anyone else noticed that HP stopped posting on this thread several months ago? To me it is the height of arrogance for them not even to acknowledge that they have a problem here, and to keep selling this printer without even attempting to fix it. Obviously this problem exists over many different router brands, PC and OS types, ISPs, and levels of user aptitude. The very least they could do is admit they have a problem and try to fix it, instead of blaming every other piece of hardware under the sun, being snotty when their customers don't buy that tactic, and then ignoring the issue when the few suggestions they offer don't work.
Over the years I have bought many HP printers, but I will have to give some serious thought to going with someone else for the next one. Look at this thread- it is on THEIR forum, it has lasted for a year, and they still have not offered anything useful. The only semi-helpful fix possibilities I see here have come from other users, and after several days of screwing around with HP's Support system, I am thankful that there is some intelligent life here.
Wake up, HP, you are definitely dropping the ball, here.