Unfortunately yes, I have also experienced that issue with HP's site.
I just replaced our old KIP with a new HP T7100 a couple of weeks ago... While all was working on HP's site for me to download the Server 2012 R2 / Win8.1 drivers initially, last week it (the printer) emailed me that the firmware needed to be updated.
Thankfully, HP's site did come back, and I was eventually able to download the updated firmware versions I needed (two-step upgrade).
If you're in a time crunch, call your vendor or even HP directly, to ask them to email you what you need given the unavailability, etc.