Let's start with first principals.
The engine needs fuel, air and a spark to ignite them.
You have checked that fuel squirts out so hopefully that is one point covered but we might reexamine this.
Air is simpler and if there are no major leaks then you are probably fine. I would still give the MAF sensor a good squirt of quick drying contact cleaner. It is just before the jubilee clip in your picture and cleaning mine took nearly 1/2 a second off the 20-80mph acceleration test.
This leaves electrics as the probably culprit. Unfortunately no-one understands electrics as you can't fix it with a hammer and gaffer tape.
So in summary, it is probably electrics but I have a niggling thought that fuel might play a part in it too.
It starts initially which means there is fuel, air and electrics.
It then dies which suggests one of the three has gone.
Air is pretty reliable so I am discounting that.
Electrics are unexplained but in my experience they either work or they don't and once they don't work then stay not working so I am holding back on that.
Fuel is necessary and is clearly there when the engine fires but possibly doesn't continue to flow so the engine dies.
Dr WCA delivers his diagnosis
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