You've given a lot of useful detail about how and when the fault occurs and while you name three problems, it seems they all come down to the one point which has something to do with an intermittent connection related to the attenuater. Without looking at the amp it's impossible to name the fault but it looks like a manufacturing fault and probably something quite minor.
You could try sending an email to France. The designers of the layout/circuitry should get a good idea from your set of all your observations, about what and where the problem could lie. My own experience with Chinese audio is that it can be first class, particularly in board design and workmanship, though it's like anything else, there are good and bad manufacturers. Chinese products do sometimes use fake or poor quality components and that can be a problem but that's a topic for another thread. The French designer would be responsible for quality control and component choice of course,
I completely agree with JLM above:
Don't be shy, just stick to the facts, repeat as necessary, and hold your ground (no need to get upset or hostile). You paid money in good faith that you'd get a working amp and it's not working for you, they can't fix it, so replace or refund (your choice). If they don't cooperate with you, tell them you're going to Visa and tell everyone you can about their poor practices.
If you can work with the dealer it's your best option. You need to to prove, one way or another, that the fault exists. If they don't accept that, it's on to plan B and Visa. If you can't get your money back, repairing the amp might not be too hard for an expert, though I'm wondering if your dealer has those skills or is just a sales outlet?
foot note: FRMs suggestion is excellent. He posted while I was writing