hello doc ,  This happens me too  but only when i am running hot on trafic  stop and go.
You can  make a different route of gas pipe coming from pump and stay away from engine ,
or use  differnt pipe-   not the steel pipe original.
The carb and gas pipe needs to run cooler . everything will cool down , will be good.
But could be everithing ... water in gas , Dirty tank , the sender unit has a filter that can be clogged, dirty carbs, float not working or fuel line filters , carb issue or  the gas tank cap has some problem and dont allows air goes to tank. 
I think you need to check some point before put the finger.
hope it helps

Next time it does it, jump out real fast and open your gas cap, but listen for a giant sucking sound at the same time.  Lack of venting in a tank is a real problem for some.  Tank either has to be vented or have a vented gas cap.  Mustangs have vented gas caps.  Some replacements do not function properly.  

Just knocking potential problems off the list..

Hornman wrote:

TKOPerformance wrote:

Vapor lock rarely effects a car that's running.  Vapor lock sets in when you shut the car off hot and it won't restart because the fuel in float bowl boils, and creates a gaseous obstruction to fuel flow.  When the car is allowed to sit and cool down the fuel condenses back into a liquid and the car can be restarted. 

When it dies can it easily be restarted?  Do you have to give it fuel to get it to restart (pump the gas pedal, etc.)? 

 
Allow me to present some alternative facts. The stock cast iron intake maifolds held much more heat than aluminum manifolds. Depending on seasonal fuel mixture the intake can get hot enough to boil the fuel in the fuel bowls of a carb. When the fuel boils, the bubbles can hold the float up against the seat, preventing liquid fuel from flowing in. The boiling fuel lowers the fuel density enough that the engine will no longer run. When the engine stalls, the residual heat in the intake continues to boil the fuel, often boiling the carb fuel bowls dry. The boiling gasoline turns to vapor and exits the carb through the fuel bowl vents (those vertical tubes with the slant cut ends on Hollies). After the gasoline vapor is vented it is nonrecoverable. These vapor vents are the usual source of the “gas stink” carb cars are famous for. After the intake manifold cools down below the boiling point of the fuel it will be possible to refill the carb fuel bowls with the fuel pump. If a restart is tried immediately after a stall, the new gas will boil. If enough gas boils away a residue of heavier hydrocarbons will remain, rather like kerosine or heavier which will not support combustion in a “modern” engine. Might run in a flathead. I knew a guy that would steal “drip” from natural gas well processing stations to run in his flattie.

All of this is why Ford provided phenolic spacers between the cast iron manifold and the carb, to insulate the carb from the manifold.

A fuel injection system is closed so there is no vent and the fuel pressure is high enough to prevent fuel boiling, so no gas stink

X-2........^^^^^...also insulate the carb.......keep fuel lines away from heat (as-much-as-possible).....remove as much heat as possible from engine compartment.
 

Triton wrote:

 had that happen to me and it ended up being the fuel filter was clogged with rust. It would run for a while the die, finally figured it out!

Sounds more likely to me, and changing a fuel filter takes all of five minutes.  With this new "gas", and I use that term loosely, you really have to change fuel filters a lot more often.  Not a bad idea to check the float bowl either.  Some junk swimming around in there can plug the needle and seat and then you're out of business until it clears.