That sure is strange.
I guess that because it stops approx. a half mile down the road, I would tend to point the finger at the carb bowls emptying out.
Does it run nice and lean and crisp immediately before stopping?
I would make sure that the fuel can flow freely into the float bowls.
Check that the fuel tank breather is not blocked.
Check the fuel lines are all good and that any inline filter flows the fuel freely.
Does it make any difference if you are on main tank or reserve? Perhaps something to do with the fuel tap??
Possibly the float bowl needle valves are sticking shut as the bike cools down?? , but that would seem very unlikely.

Well, that's my thinking anyway.
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[color=#808080][size=9]Yes,.. I too know how to waste Time and Money,...