Subject: Engine Stalling
Question:

Follow up question:
Thank you for the response. I was running the car today [it happens to be about 38 degrees out with a light rain/snow mix today] and after about 20 minutes the car idle was going from about 1000 RPM to about 1600 RPM back and forth. When I tried to press the accelerator and hold the RPM at about 2000 RPM, I could not as it kept dropping back to around 1200 then back up. Is this the fuel pressure regulator, the fuel pump or both? 
Answer: John,
You should now focus on your Idle Air Controller valve(IAC), your Throttle Position Sensor (TPS), your Fast Idle Air Valve (FIAV), your throttle body, and you throttle cable. All of those items are responsible in some way of maintaining your idle speed. Another thing to check would be your mass air sensor (MAS). There are sensors located where your air filter is attached that send signals to your ECM, which measure air flow entering your engine. If any of those sensors are sending false readings, your car will have idling problems.

Your fuel pressure regulator and your fuel pump should be checked. If you want to check these items yourself, you should be able to find a Haynes or Chiltons servie manual to help you troubleshoot if you do not already have one.

If you have a little time, a service manual, and a multimeter (availble at any hardware store for as little as $10), you can check all those items I've mentioned. Hopefully you'll be able to pinpoint your problem.
Good luck!