2001 Chevy Impala My 2001 Impala also stops with no warning

My car in the last two days stopped without warning while I was driving. Both times I was in the middle of rush hour traffic. I tried to re-start. It starts and then shuts off. My mechanic told me to keep my foot on the gas after I start the car and it runs fine after than but I'm afraid it will happen when I'm not so lucky to be in a place where I can just pull in. This morning it stopped and then the security light came on. I'm so afraid that I'm going to park it until I can get a dealer to look at it and purchase another car next week.

Does anyone have any suggestions?