(I wrote this a while ago and got distracted - I hear that verbal responses don't really help so these probably won't either, but I'll leave them in just in case).
Some other things which I found would sometimes help along with repeating the request back to them was to explain when I would be able to do the thing. So something like
"Hmm yep, you want a drink darling, I know. When we get home, we can get a drink."
"I want a drink"
"That's right, I'm driving home right now, so that we can get to the drinks. We are on the Coventry road. We will take the next right to go towards home."
"I want a drink when we get home"
"Yep, as soon as we get home we can get one. I'm turning right now. Just checking if any cars are coming - safe to go. Now we have to go up this road, round the roundabout, past the shops..."
Even if they didn't actually move on from the same sentence, it helped because it felt less like an endless loop and I was sort of narrating the progress that I was making towards the goal. Maybe on some level it helped them understand that I was actually working towards it as well. Actually I still use this with DS2 who is now 8. I don't need it anywhere near as often but he will still repeat requests, like he's barking orders at a computer, rather than wait patiently or come and see what it is they are doing. It's like he genuinely doesn't consider that you have human speed legs and thinks that you can and should instantly teleport to his side to fulfil his wish. Or that you might be doing something else which is important or might not want to drop everything to help him.
Sometimes the thing from the How To Talk books would help - giving wishes in fantasy. I remember DS1 was 3 when I first read this. I was a bit scared to use it at first because I thought that he might not understand that it was pretend and would get more upset because I was talking about giving him what he wanted but not actually doing it, but actually I found it often worked well. So I'd say things like "Ah I wish I had a special robot arm to get your toy for you." He often seemed delighted that I had understood the intention of his request even if I wasn't actually fulfilling it and would join in with coming up with more uses for the imaginary robot arm.
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But mainly the thing to help you explode less or be less stressed out by it might be to try to reduce demands of the day to day routine for both of you - things like planning outings to avoid scenarios where you're both hungry and tired on the way back. Though I appreciate sometimes it just happens and you can't always plan to avoid it.
IME the fixated looping on one thing can be quite dysregulated behaviour, esp if trying to engage with it just fuels escalation rather than helping. When my DC would be at that level of dysregulation then nothing would help either and we would quite quickly wind each other up with the slightest thing. The best book/resource I found to understand dysregulation, how it happens and what to do is Big Baffling Behaviours by Robyn Gobbel.