For a prediction about the future, they serve the same function - they both mean that it's possible that this will happen. 'Might' is more tentative than 'may', indicating slightly less certainty, but there is very little difference.

I think in your case, the usage is the same. "It might happen" or "it may happen" sound interchangeable to me. Probably "might" gives it a slightly stronger feel? There could be other cases where it is better to put "might" instead of "may", but I think it makes no difference.... usually. "Sir, might I go to the library?" sounds strange to me, for example.