Electrical Problem. installed a carriage house 2. Light kit works, fan does not. took apart,

Question

installed a carriage house 2. Light kit works, fan does not. took apart, investigated... white electrical connector between fan and light kit sparks blue... fan runs. wiggle some more, fan stops, wiggle some more, connector "lights up" fan starts... and so on.. I'm not sure whether its the light kit side, or the fan side, or both. But... any advice?