Finally some progress
I enabled user registration in Wordpress and created a new user with my test email address which I always use in this scenarios.
When using the WP signup page I received the error that the email address did already exist in the phpbb database. I found an old user in phpbb that I created for several years ago, removed it and bang it works.
So far so good, the difference here is that the default wp page stops and display the error while the wp-member registration probably stops, but not displaying the error so the user think the registration process succeeded.
Then I started to look at real users that complained about the registration process and found that those users had accounts in phpbb created many years ago, long time before we started with Wordpress but not used the for years.
But it's still strange that this behavior started in February unless the check email function is a new feature.
Edit:
The function "The function "Enable/Disable check of the email in phpBB before it is updated in WordPress (front-end plugins pages)" was disabled also.
/Tomas