82 Fiat 124 Spider Starting Related

I've got a 1982 Fiat 124 Spider, originally equipped with a turbo (removed) and has fuel injection, traditional distributer cap, that has a problem. This car is stored in the Winter and I do put a fuel stabilizer in the tank.

When it is cold, it seems to start no problem and runs ok most of the time. However there are times when it either dies at idle at a stop light, or very infrequently it dies going down the road at cruising speed. Once this happens it is a bear to get started again. I've also noticed that if we stop some where, for 20 minutes or so, it can also be very difficult to start. So I tend to think the restarting problem is associated with the engine being warmed up. Eventually after much cursing, I do get it started after the battery is all most dead.

So I'm considering different possibilities-
-Water in the Fuel Tank.
-Intermittent Electrical Problem
-Intermittent Fuel Supply Problem (pump?)

Regarding water in the tank, I have added a fuel additive called SeaFoam which I was hoping would take care of any water.

What really is frustrating is that a couple of years ago (yes it's been doing this for that long) we took it into a foreign car garage and they could not get the car to do it (display the problem) for them. Maybe I need to go to another shop...

Any ideas? Thanks! :)