I'd recommend a diagnostic check to see what fault codes flag up. It could be the fuel pump, MAF sensor (would run rough before cutting out though), cam sensor, lambda sensor.
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It'll have to go to a dealer or an retrofitter like autologics could do it. But expect to pay £600.
Just had all mine done. Along with the glow plug relay. Only 3 of the 6 were working on mine. Also don't get cheap ones. Get bosh or NGK. Bosh are what Audi would fit when car was new. And it's bosh I went with.
I've heard horror stories too from carbon cleaning. In my experience keeping on top of maintenance is what keeps older Audi's going. It's not cheap but keeps mine reliable.
Sorry to hear this Tony, thankfully there's a large variety of products available which are often used in the classic car scene. The hardest bit would the carpets as the whole interior has to come out.