John / Bryan,
The following is my understanding of the Rotax system.
The alternator on the Rotax is a fifth pickup coil along with the four ignition coils integral to the engine. Two leads come from this to the regulator which is a separate electronics module which does the rectifying (ac to dc) and regulating (determining when to charge the system). I personally expect that if there is a failure in the charging system that is is with the regulator module. The good news is that unit is external to the engine and fairly easy to replace or possibly remove and have tested. One possibility is that the system only squeals when charging, therefore it should occur more frequently if you put more load on the electrical system (lading lights etc). Another possibility is the big-ass capacitor that is connected to the output of the regulator (cylindrical part ~1" diameter couple of inches long) has failed or become disconnected. I do not how likely that is to be the issue but if it is it is cheap and easy to fix.

Intermittent gremlins are the worst, good luck.