And then how long before you can get it to start again? This doesn't act like a dirty or faulty connection sounds a lot like a failing electrical component in your ignition system which works marginally, heats up quicker than it should, and then quits working at all til it cools back down. Suspects are the ignition box (ICU/ECU, mounted over on the driver's side at the rear of the engine bay), the pickup coil (inside the distributor), the ignition switch, and the ignition coil (not as likely, especially as it's been replaced recently).
If you want to try some diagnostic work rather than just shotgun-replacing parts, fetch a hairdryer and some basic tools. Start the car to verify it will start, then shut it off. Remove the distributor cap and aim the hairdryer, on a hot setting, at the pickup coil for a few minutes; get it good and hot. Snap the cap back on and try to start the car. Does it start? If not, replace the pickup. If it does, then shut it off again and heat up the ignition box with your hairdryer. Get it good and hot. Try starting the car. No go? Your ignition box is faulty. Yes go? It's something else.
Much more difficult to heat up the ignition switch to test, so this diagnostic technique has its limits, but you can also do the opposite: engine stops running on its own, remove the ignition box from the car and put it in the freezer for half an hour. Put it back in the car; does it start?
Also, watch your inbox for a PM.
