2005 Buick Terraza Vehicle will not start

Have you heard on any problems with the vehicle not starting intermittently? My wife drives this vehicle daily, and at no certain times, the vehicle will not turn over, or even "click" when turning the key. She will continuously take the key in and out, and keep trying to start the vehicle. The vehicle starts anywhere from 2-20 mins. Later. I have had the vehicle in to service centers, and they cannot find anything wrong. I have been told until they can duplicate the problem, I am out of luck. This is really embarrasing to her, especially when she has coworkers/friends in the vehicle. We recently went out of state, and the vehicle did it again. We had a tow truck coming to help us when it finally started. I have checked the batter, the connections and the starter, and cannot find a "smoking" gun. Hopefully you have heard of this condition.