how can i fix my fiat punto mk1 1999?

my t reg punto has recently began playing up to the point where i refuse to drive it... but cannot seem to get it fixed even in a garage! sometimes when the revs drop, eg. when waiting at traffic lights or when stopping behind another car, the engine cuts out. Rather than starting up right away when i turn the key, the engine itself is totally non responsive untill i have tried literrally for minutes to get it started (by turning the key repeatedly). all of a sudden the engine kicks in and the car continues to drive, seemingly as if the problem never existed and without problem.... untill the random fault occurs again when i am in a situation when the revs drop.
I have taken it into my local garage who have examined the engine thoroughly and found no problem at all with it. They referred to me an electronics specialist. After having the car for 2 days the specialist admitted that they too could not diagnose the problem, as this would involve hooking it up to the computer and simulating the intermitting fault (which they could not get to occur once hooked up to it). a friend of mine who is good with mechanics suggested the coils be changed, which he has done, but this seems to have made little difference. Im literally stuck and no one seems to be able to help. Could anyone suggest a possible cause of this problem? many thanks