This has been a very strange problem right from the start. You have done some good diagnostic work there but I think you are drawing some wrong conclusions from what you found.
Your findings definitely suggest there may be a time related side to the problem and that is worth investigating. Heat is an obvious factor to consider, as is component ageing. However, it is very unlikely that a modern resistor will change its value so much that it would cause things to trigger like this. A carbon composition resistor worshipped by those "velvet eared" gurus for their superior vintage tone
WILL eventually do that, but modern metal types will not. Modern resistors outperform these bits of old rubbish in every way including sound. If you really want that "softer warm" tone you can design it in with modern circuitry. In good design you set things up to be as precise as possible but also as uncritical as is possible, in other words you leave as wide a margin for error and drift as the circuit will tolerate, and you use components that are in the middle of as wide a range of acceptable action as possible too. With the exception of the valves the quality of components in the H&K amps is high as is the build quality. The use of Chinese valves is a deliberate choice by H&K to sensibly keep sales prices down as they are aware that people generally swap them out at the first opportunity for their own particular magic models regardless of what was originally put in. There should be no problem with this occurring due to thermal drift.
Again a common myth is that "Eastern" PCB manufacture is not as good as our own. That is so much hogwash. It depends, as it does everywhere, on the particular company who is contracted to make them and the price paid. There are poor quality ones out there, if you want to pay peanuts you will get corners cut by monkeys. Most mainstream manufacturers are at least as high quality as anything in the West, often better. For example, how many eastern made mobile phones do you see being tossed because of their cheap eastern PCB problems?
People incorrectly believe that, because the top of the amp gets hot to the hand that means the interior must be under thermal stress too. Most components are perfectly happy to work at a temperature which would burn your hand. Yes, their lifespan is reduced at higher temperatures but this needs to be seen in perspective. Reducing an electrolytic's 50,000 hours lifespan to 30,000 hours say is not a great loss in real terms. We did some research into this here on the forum a long while back to look into that claim. One member used a thermal gun thermometer to accurately measure internal temperatures through the vents so the amp stayed closed as in normal use. The core of the amp, the lower undersection carrying all the PCBs, stays very cool even under high output drive. And yes, the power soak resistors are in there but, if you do the maths correctly, you will find the maximum amount of heat they could be required to dissipate is not high at all and it does make no difference to the temperature inside in practice. The top section which we can see into heats up, but the case is designed to conduct the heat upwards and outwards acting as a heatsink. The vast majority of the heat is produced by the valve bodies and will of course rise in that space. They are out of the bottom section in the heatsinked upper cavity so little is carried downwards to affect the other circuitry. Conduction heatsinking like this is a much better more efficient approach than using an insulating wooden box with a few slots or holes punched into a backplate which you hope gives some air convection and generally doesn't. Internal temperature is NOT an issue with the H&K amps. Time has proven that, as heat related failures are not occurring even as frequently as in other mainstream amps out there.
It is conceivable that one of the electrolytic capacitors could have aged prematurely though it is not likely. All components can conceivably have faulty items at manufacture but, to stress again, their reputation is given by those who know nothing of how they really work and how they are accurately specified. The symptoms do not really point to this as a way of locking up the amp until an immediate restart fixes it. Drifting trigger voltages would more likely cause a function on the amp to activate but would leave it in a state where it would still respond to other controls in some way.
It is possible that you have an intermittent connection at one of the PCB cable sockets. This would only need to be split then remade to correct it. The connectors used are high grade types commonly used in other areas of electronics requiring high reliability without any issues. I do not think the connectors themselves would be the problem but it is easy for a tech to try.
It is also possible that you have a cracked solder joint, though again not likely and I will point out that this does not happen anywhere near as often as "internet common knowledge" will tell you. PCBs ARE THE DEVIL'S OWN WORK is the current mantra with guitar gurus and their acolytes. It is absolute and total bullshit. As an electronic engineer of many years experience I can tell you they are more reliable in use, more accurately designable for better sound and more consistent in that than any hand built rat's nest. Many techs hate them because they do not generate as much money and kudos as working on that "mountain spring crystal clear top, elfin bell middle and grunting bottom" pile of spaghetti which anyone could service with a cobbler's hammer, an electrician's screwdriver and a plumbers gas torch. With good equipment they are more logical and easier to work on, if you know what you are doing!
I do think the only thing you can do is to give this amp to a tech and get him to try to trigger the fault then see what state the various lines and components are in. Other than that you are left with changing out PCBs one by one until the problem goes away. With surface mount components the idea of hand repairing a board is pretty much a losing game, they are far too awkward to easily work on. That is one downside of owning a modern design amp I'm afraid. It is possible to repair, I do it myself in some of my own builds, but it is much more time consuming and less reliable than manually working with through hole components is.
My gut tells me this should be a problem in the digital uProcessor area on that board. As I said, I can always be wrong on this but for me the locking up suggests the digital circuitry being thrown into a state which is never seen in normal use where it cannot recover. The only way to test any of this would be to set up the amp with the PCBs exposed and trigger the fault then to explore the PCBs looking for something unusual I'm afraid. The oddity here is the locking up of the system. A voltage drifting to the point of incorrectly triggering the amp in a natural designed fashion would not cause that. I suspect this is a hard fault somewhere in the digital circuitry rather than components in the supporting or analogue circuitry going out of spec. Though, as I said, I could always be wrong on that score of course. We need someone to take it on with that in mind.
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still 0.