It Starts, then Dies, then starts again...(Engine)

[cmyst]

I have a '93 G20, no modifications to the engine were done, but recently did a complete tuneup. The issue is that when I drive the car for short errands and turn the engine off to leave (usually within 10 min to 30 min), I would try to start the car and then it would die. When I start it again after it dies, it works again. This happens everytime I use the car. Is this the start of a major problem?
The Rpms drops to zero when the car dies at the first attempt, but works like normal when restarted.