My 63 Valiant

Any other symptoms?
How does it stop running?
Just idling, or is there some driving during those 15 minutes?
Loss of power, more loss of power, then dies? Or just flat dies?

Back to basics. One possibility is trash in the fuel, clogging the filter. After choking the engine out, it may settle out and allow it to run later. Fine rust in the gas tank can do this.

If the car has been retrofitted with electronic ignition, a faulty module can also cause problems as it heats up.