Audi stopped working after 10 minutes running and after 15 minutes started again.
 

Hi guys, I'd really appreciate if one of you could help me with a problem.
I own an convertible 1.8 Audi TT 2001 5 speed. something very strange is happening and i can't fins a solution.
Around 3 month ago i was driving my car for around 10 miles than i parked at a local Walgreens. 10 minutes later when i left the store i couldn't turn on the car. it was like it had no gas. the ignition was working but the car won't start. i made a phone call and about 10 minutes later i turn the key again and it worked, like never happened. i found it very strange but the car was working fine.
same thing happened three or four times again in a period of 3 months, but this saturday when i was driving to a local mall (8 miles from my house), i was stopped, waiting for the green light in front of the mall, the car died. same thing, turn on the key, it looked like was no gas. i was stopped in the middle of the street, i lived alone and after 20 min the car started again.
i was driving back home and happened again in front of my house, after the same 20 minutes the car started again.
i have no idea what it could be. i took it to the mechanic, he ran the scan and nothing show up.
it is an old car, Audi want to charge me $250/hr just to look at it, with no guarantees.
i believe that might be a sensor related to fuel or something. have one of you guys heard something like that before?
Please a word of advise.
Thanks