I have a similar problem. It has been fine for 2 years, then I changed something (can’t remember what) – and now emails are not being sent with passwords when a Free member registers. Tried resetting everything back to how it was. But not working.
Run a WP SMTP Mail plugin – did test. Email not sent.
Can’t think what it is.
http://www.internetmarketingbootcamp.org
Register under MEMBERS in the MENU to test.