Chrysler Repair: 1999 Chrysler LHS:intermittent shut down, 1999 chrysler lhs, chrysler lhs

Question
I purchased a used 1999 Chrysler LHS last year.  It has been a pretty good car with some problems that haven't been too bad to fix.  However, I am experiencing a new problem in that the car will shut off, without notice, anytime, anywhere.  It just shuts off and sometimes, it can be restarted immediately and other times it can take up to 20-30 minutes to start.  Just before this problem started, I had a new battery put in because it still had the original battery and the car died in the middle of the road.  I had it towed and the mechanic put the new battery in, but now I am not so sure that was the problem.  Since that repair, the car will shut off it will just stop.  The lights, radio, windows and everything else works, the car just stops.  Every once in a while, a code will pop up on the odometer when the car stops and the code is P1684.  I looked up that code on About.com:Auto repair and it showed that code which is "Battery disconnected within last 50 starts".  The first couple of times the car shut off, we gave it a jump, because we thought it was a dud battery, but with all other electrical working, we were told it was not that.
Can you help me?  Have you had others complain about this particular problem?  Any answers you can give me would be greatly appreciated.  
Sincerely, Lauren

Answer
Hi Lauren,
There are a couple of possibilities:
One is that there is a flaky contact in the ignition switch that is cutting the power to the powertrain controller/spark coil/fuel pump. You would need to notice whether when you move the key to 'run' (before trying the 'start' position) whether the hum from the fuel pump located under the rear seat is heard for about a second or so and then stops, which is normal. It starts again when cranking, ideally, but you often can't hear that. So listen for that now, and also when you have a stall to see if it is different (i.e. no hum).
The other is that one of the sensors of the position of the cam and crank shafts is breaking down when it warms up and then self-repairs when the engine stops and cools. That can happen without setting a code, for a while, but it will soon be self-detected by the controller and set a code: 0320 or 0340, respectively. So if you are near an Autozone parts store keep checking the codes (for free) after each failure.
All these possibilities can be diagnosed with a voltmeter while the problem is present but not when things are normal. Let me know if you hav a voltmeter and want to be prepared to test for them the next time it shut down. Also tell me which engine you have.
Roland