I have a 2002 Ford Taurus and I am trying to figure out what is going on with my car. The problem started about 2 & 1/2 months ago. I was parked listening to the radio w/ my air on an my car randomally shut off. I had to wait before it would turn back on. (it wasn't the battery) the same thing would happen once every week to week and a half. Now, it is more frequent. It will shut off anytime the car is in park and running for more than a minute and will shut off when the brake is applied for about the same amount of time. I usually am able to start it right back up. I know I need spark plugs changed if that could possibly be the cause? I'm also going to have my battery checked today. I'm just trying to figure out what the cause is so I can get it repaired before whatever it is gets worse or completly goes out.

 

You don't tell us how many miles yo have on it and which engine you have in it (3L or 3.5 L with 24valves?). But you give us a hint by saying the plugs need changing. It may mean that your car needs a complete tune up, which should include:
oil and filter change
transmission service
plugs, wires and maybe even the coil pack
serpentine belt
use a fuel system cleaner for a tank or two
replace air filter
clean MAF sensor
change engine coolant
battery check or replace if old
check all ground connections and straps
replace brake fluid
check brake pads/shoes for wear
check calipers for free floating, clean sliders if they don't float freely


Once you have done the engine related things and you still have it cut off we may have to check the fuel pressure.

BTW you don't have to do this all at once, but get going on this list.

 

It has a little over 200,000 miles on it an I just had my oil changed and battery checked today. My battery was fine. I'm replacing the spark plugs once my rear spindles and struts, & front inner tire rod ends are replaced. I'm hoping spark plugs fix it tho. If not, I will look further into that list.

 

In trying to examine the symptoms you describe something kinda crops up and that is; when the vehicle is at low RPM the charging system is also at lower output. There just may be a questionable connection that is overcome by the charging system when the RPM is higher and output is higher also. Soooo, I would suspect that there is a connection involving the power to either or both the ign and fuel system that is possibly causing enough of a voltage drop that the vehicle just quits running.
Bluewind gave you a good list of things to check and among the higher priority ones would be the power and ground connections. I would start with every ground connection you can find and see and loosen and then retighten it. Then you can start checking the power connections namley the one from the alternator that goes to the battery. Poor connections cause some weird results and your vehicle may just have one.