If we have a class that we want people to register for -
since dt register doesn't support repeating events, we have to create a single event for the first class. But then after that date, it doesn't show up anymore in the list of events you can register for - we want to allow people to register after the first class starts.
Well, I assume you are running events on multiple days. You just need to modify the date range of the event... keep the start date but make the END date whatever the last day of events is. The registration will remain open until the LAST day of an event.
I'm not sure how you have everything configured, but using the Copy events feature, you can easily and quickly make multiple occurrences of an event on different days... making the recurring event feature not really needed. This way you have separate occurrences allowing you to tweak each one as needed, but first you can create one event and then make multiple exact duplicates.
Or... just change your end date if your current setup works fine for your needs