As a former sysadmin and a [still, for the moment] reddit moderator, my bet is that most of the subreddits that switched to private forgot to (or didn’t know to) go into “new reddit” and switch off the thing that allows people to request being added to the now-private subreddit.

A HUGE influx of people pounding on the “let me in, add me to the sub” button, which sends modmail, may have overloaded the whole modmail system, which in turn sometimes goes kaflooey for no apparent reason (my theory is: it gets bored).