Neutral Safety switch problem???

I have a 91 Olds 98. Car has been running fine for a long time till today. I was going around 40 mph early in the morning and the car stalled, or just cut out.. While coasting I put the car in neutral and tried to start it, but it wouldn't crank. I pulled off the road, put it in park, and it started back up, but ran poorly for a half mile, then ran fine. After work in the evening, I pulled codes and got code 31 (PRNDL Switch circuit problem). I noticed that the car only starts in Park, and not in neutral, (nor Drive, reverse, or low, as it shouldn't). I let it idle in my driveway for a bit and it just cut out twice more, but started right back up no problem and idled fine. I cleared the codes by disconnecting the POS terminal for 30 seconds like the service manual says, and let the car idle for awhile, and it did not die out anymore. Took it for a 10 mile ride, and it ran fine, and I re-checked for codes and 31 was no longer there, just code 12 like normal.

I have two questions, the car should start in neutral, right? And if the neutral switch is faulty, can it cause the engine to die out?

I think you have 2 problems, possible bad neutral switch and something else. I would look at a possible carboned up throttle body or weak iac, also maybe carboned up, the quick restart usually points to this as a starting point.

Just finished cleaning the throttle body, which wasn't too dirty, and the IAC unit, which was caked with carbon. Put it all back together, and 15 miles later, seem's to be running strong, so hopefully that was it.

As for the neutral switch, I'll have to order one. Are there any risks to NOT having the ability to start the car in neutral? Thanks to maxwedge for the quick reply to my problem.

Well, ten days later, and today it coughed while waiting to make a left turn. When I got home I let it idle in the driveway and after around 10 minutes of running smooth it started to sputter and then it stalled. Started it right back up, and it sputtered a bit, then smoothed out. what do you think should be the next step? Thanks in advance for any help you guys can provide.