WHY DOES MY CHECK ENGINE LIGHT COME ON THEN OFF

You may have an intermittent problem, so when the on board diagnostics system checks it - sometimes it checks ok within the parameters set, and sometimes it's not, which triggers the check engine light to come on. The codes will be stored in the history or pending, even if the light is not on. Have the codes checked to make sure something critical is not neglected, leading to a more expensive repair. Simply you can also check to make sure you are tightening your gas cap properly, because if it is loose the check engine light will come on.