In general, the stator either producing the power, or it's not and the system will have trouble charging and staying running.
If the rectifier is getting really hot, this is typically due to a bad connection on the output side, most likely the ground, but it could also be the battery side. The high resistance from the bad connection causes the rectifier to fail.
I would check all the connections from the rectifier to the battery and ground first and start there. You might just clean them all up and see if that helps.
After that, you could also put a meter between the battery positive terminal and the connection there, and see how many amps it's drawing. Something could be drawing too much power, more than the rectifier can handle.
