Hi,
This is a fairly common Fiat Punto pre-2000 problem.
I had the same problem on my Punto 75 SX (1998). The problem started last winter and it only happend directly after starting the car at first. This summer it also started to happen when the engine was hot. Two local FIAT-workshops couldn't find the source of the problem and I had the coils, the lambda and the spark-plug-cables replaced.
I found the solution myself. The metal parts holding the ECU in place looked rusty, as well as a screw that connects a cable to the body of the car next to the ECU. I unplugged & removed the ECU and cleaned all the parts (including the sides of the ECU) with sandpaper. This solved the problem on my Punto.