I would not be so sure about the problem being just these 'few' models. Every service tech out there has to be careful what they reveal about such issues because they could lose their licensing contract if they go around bad-mouthing companies or telling the customers all about the various failures. I know. I used to work in electronic design engineering and the one thing management never wanted me to do was to walk up to someone and honestly admit that me made a serious design error - not even to our own design lab technicians that were debugging our designs for us!
I have looked into this Onkyo HDMI/graphics problem for months now as I built several home theater systems with used Onkyo receivers. While investigating features and prices and history, and after I purchased one that turned out to be already failed plus another that is in the process of failing, I saw complaints about Onkyo HDMI failures all over the internet, on store customer reviews and audiophile forums etc., about HDMI failures on many of their other models too, even including an HDMI failure on a dedicated audio processor indicating that the problem may be inclusive of nearly ALL Onkyo components with a built-in HDMI input switch DSP and graphics processor board.
My inspection of my Onkyo receivers indicates that none of mine have either an internal fan nor any heat sinking on the video controller, which is the hottest item on the board (probably) but it also contains one, two or possibly three digital signal processors too on the HDMI board with no heat sinks either.
The capacitor temperature rating on Onkyo components is standard commercial rating of 85C, according to the claims of those who have posted the official Onkyo service memo on the 606 HDMI failure to Youtube etc. and who also recommend using the 125C rated industrial/mil spec capacitors instead of stock components (I even found a similar ebay HDMI repair service like the one already linked here). The failure is that the linear regulators start oscillating so the output capacitors are losing a significant percentage of their charge storage capacity. The HDMI board could be re-spec'd with heat sinks on the chips, fans, and/or high temp caps or more bypass cap, at a minimum premium pricing of a couple of dollars to tens of dollars per thousand, depending on the model.
So, particular units fail at varying rates and ages, between the three cost-cutting decisions to use lower temp rated capacitors that dry out under heat eventually, plus no heat sinking any of the heat-generating IC's on the HDMI board, plus the omission of any sort of cooling fan. The varying failure rates between different models could be related to whether the model has a cooling fan installed, whether the case of particular models is more packed and holds more heat in, whether the HDMI board is larger and thus a better heat radiator, or has more DSP chips on that particular model raising dissipation, if there was any variation in capacitor reliability characteristics of the particular production run, etc. all these variables may translate into varying failure rates among and within models.
Most likely if you do not install fans inside your unit when you first buy it or at least add a cooler plate fan on top of it (if it has no internal fan of its own), the thing likely will fail eventually REGARDLESS of the model number or year of manufacture.
This sad state of affairs will likely continue, until Onkyo decides to do something about this design defect that even kills their higher-priced Integra line on occasion according to the guy on ebay who repairs them.
Insufficient cooling is not an Onkyo-exclusive problem.
Their Onkyo receiver prices seem to be about the best for the feature set they provide, but after having bought several used Onkyo receivers that are all exhibiting this HDMI failure to some degree ranging from mild and intermittent to hard failure, I have to say I am skeptical whether they will ever do anything about this problem.
The Onkyo HDMI board really needs some glue-on heat sinking on the graphics processor and the DSP(s), more air flow/vents around the board, and/or maybe a fan aimed at or even installed on the HDMI board, rather than just mil spec capacitors. After all, your PC/laptop has heat sinks and fans for the video! Why not your receiver too? Why should your HDMI board be hot enough to cook eggs on?
The way I am shopping for my receivers is, since the receivers all fail anyway (in my estimation), I am simply buying them used dirt cheap off Craig's List and repairing the HDMI by changing capacitors myself once the failure gets too severe for me to use it any longer. Unfortunately the top-of-the-line models are rare on Craig's List, they cost too much on ebay, and they do not adequately reflect the devaluation from the failing HDMI problem in my estimation. Then again I am a known cheapskate. I am still shopping for my ultimate receiver for my living room.
There are a ton of these Onkyos on Craig's List all the time, including some of the newer networked models with 3D and 4K are seemingly exhibiting this HDMI failure now, and when confronted with the failures and all the evidence on line that it is a continual problem with Onkyo the owners sometimes dump their Onkyo receivers incredibly cheap in frustration and decide to buy Denon or Marantz or Yamaha or even a sound bar etc. instead.
Problem is, even those other brands are having some failures too because capacitor manufacturers are playing the same specmanship games that everyone else is, rating their tiny surface mount components with ridiculous reliability, microfarad, voltage, and temperature specs simply because everyone else is doing it too. Almost all electronics are experiencing premature failures at various rates because of this capacitor problem. It is one of the prime sources of consumer electronics failures.
I even know of people that have ditched surround sound entirely and gone with huge monoblock tube amps or rack mounted solid state professional quality amps, and vintage tuners or receivers with no DSP at all, because this more primitive technology is so much more reliable and DSP is overly complicated and costs too much and fails too frequently.
What would I do if I had a failing Onkyo? Well I do have a few of them. If I were technically skilled (as I am) I would just keep an eye on the problem and then when it fails entirely or gets so bad it is essentially unusable, change the caps on the HDMI board with high temp leaded caps, and see if it fixed the problem. If not, buy something else.
In fact I am doing just that, except I am taking a short cut and buying all my Onkyo receivers used off Craig's List to save money - tons of money - instead of buying new and paying double or triple or more for the pleasure of owning a receiver that I will end up repairing it myself after the warranty expires anyway.
If I were not technically skilled I would skip step 1 and jump right to step 2 in all cases - buy something else that is not Onkyo, at least until their reliability of their HDMI boards improves. It is not worth the cost of having to spend so much money repairing it after the warranty expires.
The Onkyo authorized repair is going to be exact replacement parts, not upgraded parts. No technician is going to get creative with his repairs and risk losing his franchise.
Even the e-bay upgraded components and discounted price repair service is expensive - you still have to ship your receiver round trip at your own cost and prepay the repair, and there is no guarantee it will come back fixed - depending on what happens to the person doing the repairs, it might not come back at all - and then even if it does come back repaired, all you have is the same old obsolete Onkyo receiver with over $100 of added shipping and service fees that you will never recover in a used equipment sale anyway. Better to put the money toward a new, competitor's receiver.
If you are really attached to the thing and just cannot find anything affordable to replace or upgrade with, maybe the ebay repair is a possibility.
Still, (due to the prevalence of the problem) the only truly cost-effective repair for the HDMI is if Onkyo does it for free, or you do it yourself for the cost of parts and just donate your time. I believe Onkyo is being so good about repairing out of warranty receivers if they are less than a year out of warranty because they do not want to fix the design and they do not want a lawsuit.
So Onkyo receivers need to be treated with care, kept as cool as possible, and if the HDMI fails, either have Onkyo fix it on warranty, or fix it yourself with better parts, or have someone on ebay fix it for you cheap, but do not bother with factory-authorized service out of warranty because it is too expensive and they use the same failing capacitors anyway without any additional heat sinking fan or any additional cooling at all.
I repaired my own HDMI board with capacitors as old as I am, huge old aluminum electrolytics twenty times the physical size of the original (or more), and they have huge series resistance due to their size. They are basically worthless as high frequency traps yet they fixed the problem.
If you are running with the original design or even one that was repaired by Onkyo already, you should definitely keep the receiver out on an open shelving system and put a cooling plate with a fan over/under it, build in a fan, or point a desk fan at it from close range, to keep the temperature down, or it will probably fail again.
My $.02 plus a couple thousand for inflation.
Sorry for blabbing on and on, I tend to do that.