Hi
I kinda had the same problem on mine, only mine dropped back to idling speed when the warning came on, it ended up being the throttle body which i had replaced under warranty.
Id certainly take it into fiat and get it looked at, you dont want your car to stop working when your drivin along, trust me its not a nice experience.
2002 Stilo 1.6 Active, almost debadged and i have big plans!!!