If I had to make a guess, I'd say that, as the thread suggests, it's heat related.
Running any 2-cycle up or down a hill is going to heat things up. Up the hill, the increased load builds heat. Down the hill, the tendency to keep the throttle closed limits lubrication, which also builds heat.
The solex uses a combination of free-air and forced-air cooling. When you come to a stop, the free-air part decreases quite a bit.. no more wind moving through those little fins. Heat stored in the top-end is free to migrate throughout the engine, and to things like the carb, fuel pump and (metal) lines.
Are solex prone to vapor lock in high-heat? They use a fuel pump, so I'm sure it's possible. Just one bubble in that line between the pump and carb, and you will stall.