Brakes sometimes don't work when I first start the car

I have a 2004 Ford Taurus. The brakes sometimes don't work when I first start the car. It's an awful feeling to be pressing the brake with my foot as hard as I can and the car still rolls when I put it in gear. I first took the car to a Sears repair shop. They couldn't find a problem with the brakes and the issue didn't show itself when they first started the car up, which is when the problem occurs for me. It's now at a Ford dealership. It's been there for over a week. Each time we've let the car sit a little longer. Each time the technician doesn't
experience the problem so he can find it. They're frustrated with me because they want me to pay the diagnostic fee and get the car out of their lot. I'm frustrated because this is the car my 18 year old son drives. What if the brakes give out while he's, say, on the expressway and needs to make a quick stop? Everyone in this family has experienced this issue. Have you ever heard of this happening before?