The bearings on the pulleys might be going bad, causing the belt to slip and therefore not recharging your battery while you are driving. I had this issue on my 95 SE Turbo, until on of the pulleys failed completely and caused a belt failure.
I am unfamiliar with a saab - just looking in to getting one... but I did have a similar problem with my old Toyota Celica. It would shut off at random while I was driving it - especially in the rain!! Nobody could figure it out (new battery, new alternator) they wanted to run all kinds of expensive diagnostic tests. A buddy of mine suggested I get a new "z-coil" (or maybe c-coil I don't know it was a long time ago). Anyway, that did the trick! I drove the Celica for an additional 60,000 miles! Hope that helps?
Same problem w/2000 Saab SE Turbo convertible. Fuel line and DIC replaced on recall. Since then; intermitting not starting with no apparent reason. Alternator replaced, turbo boost pressure valve, idle control valve and vacuum lines. Third trip to dealer for repairs in 30 days, this time by tow truck. The Service Department has not called today; but let me guess, it started and they could not locate any problem.
Oh, I almost forgot, a new battery just before replacing the alternator.
I had a similar problem with my Toyota Celica and Honda Accord. It ended up being the coolant temperature sensor. One big clue of that though is if you are getting horrible gas mileage. What it does is reads the temperature of the engine to see if your car needs to run rich (which it does when its cold). If the sensor is broken it will think that it is constantly cold and will constantly run rich, which causes the engine to shut off.
Not saying this is the answer, but it's happened to me more than once.
Try checking the Alarm/security system, this happened to a past car of mine and fixed the problem immediately.
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