What are possible causes for intermittent rough idle and******** while engine is cold?

Sometimes once or twice a week, sometimes once a month when the car is first started it has very rough idle and while driving it will***** and the check engine light blinks on and off. After the car warms up (less than 10 miles)it runs fine and engine light stays off. Don't know how to diagnose because it isn't consistant and it never happens when I can get to a shop. Also, when the engine light goes off will the code that caused the blinking be stored or is it gone?