That could be a sign that the MAP may be failing on a TBI motor. Any other times that it starts running rough or smelling rich at idle?
The tbi system is pretty simple. It gets a signal when cranking from the ignition switch to fire the injectors. It's critical that it gets a good 12V from the ignition to send that initial injector fire signal. If the battery is too low it doesn't send the signal and the car can be very hard to crank over, but once it catches and the ECU is powering the injectors it will run fine. Also bad grounds will cause this process to get messed up as well.
That signal goes from the ignition switch to the ECU (via the pink wire in the main loom) under the hood. Check for chafing on the wire bundle as it crosses the manifold to the firewall. Sometimes the shielding gets old and the wiring wears through, but that's rare.
The last items is the control pressure regulator can leak. It's in the TBI unit and after time it can leak and cause excessive, or no fuel pressure conditions. However it's normally a rich condition when they fail. The circuit is a simple supply and return to the tank. The fuel pumps do go bad at times, but normally that's a no start condition at all times.