could there be a problem in the electrical hornest that causes this problem?

Did you ever find the problem? I have the same model car with 190K that just recently started doing the exact same problem you are having.

What engine do you have and does it have a distributor? then I try and help you. I used to work at a GM dealership, but I need to know what kind of motor and ignition system you have. let me know. Ok, I am pretty sure that this car has a coil pack ignition system. Under neath the Coil pack is the Ignition Module. I would suspect this. Do you get any Check Engine Lights especially a code 42 which is a loss of electronic spark timing. When the car dies, do you have spark? Does your car have a Check Engine Light on? There are several sensors that can cause a lack of fuel delivery by the injectors. 2 of the most common are the Mass Air Flow Sensor and the Throttle Position Sensor. Since you have spark, the Crank Sensor has to be working but even though the engine is getting a Crank Signal, it may not be able to fire the injectors for several reasons. If you do have a code, check to see what the code is because it may allow you to trace down why the injectors are not being opened.

I replaced many components including the fuel pump in the gas tank in a mini store parking lot using a adjustable wrench and and hammer! No results. Changed the ingition module and every thing is running great on my '92 Chevy van with 267k miles. My two sons had the same problem and solution and a certified desiel mechanic where I work. All with GM engines. Told them all to replace ingition module and all have been repaired. Cold engine bypassed the module and when warmed up, runs through the ing. Mod.

try replacing your thermostat.. probably costs like 10$ if its not reading right, it will cause your engine to stall for a while.. we had the same problem as you but with a 99 blazer.. after replacing the thermostat, all is well!