A couple of things…

• The logged in menus extension is no longer developed/supported – its features were rolled into the core plugin in 3.2
• This functionality relies on the “theme_location” arg in the wp_nav_menu() function. This value is set using the wp_nav_menu_args filter. Since it’s a WP filter, other plugins can (and do) hook into this as well as other filter hooks in the nav menu function that come later. It is possible for other plugins to “blank” this value or drop it altogether and that has been the case in other situations where people have indicated that it does not work. Unfortunately, when it’s a conflict of that nature, there’s not an alternative (other than dropping the offending plugin, which in this case is probably something you don’t want to do).
• WP-Members 3.3.0 (which is currently in beta) will offer a new (and much better, IMO) setting to manage menu items individually rather than entire menu as a whole. The logged in menus feature will remain for backwards compatibility/legacy purposes, but the new setting will be much better. It is also more likely to work in situations like this.

Any idea on 3.3.0 release date for production use?

I can’t really set a date. It’s out as a beta, so it’s fairly complete/stable. But this is a very significant update and so there are some things that still need more testing.

As of this writing, the first release candidate is out. There are some adjustments being made based on testing and feedback with RC1, so RC2 will probably be pushed out later this week.

While most of it is fairly solid at this point, the primary concerns are (1) maintaining CSS settings during the upgrade and (2) registration when completed through wp-login.php or another integrated solution (other than WP-Members native registration). So for many applications, the beta can certainly be used if it has been tested in a staging environment. I wouldn’t recommend simply updating a production site without some testing first at this point. But it’s OK once tested and there are no known major bugs (outside of what I mentioned above).

Release information and announcements can be followed here:
https://rocketgeek.com/release-announcements/

3.3.0 RC 1 information can be reviewed here:
https://rocketgeek.com/release-announcements/wp-members-3-3-0-beta-release-candidate-1/

Current beta release (which is RC1 as of this writing) is available on wordpress.org by going to the plugin’s advanced page, scroll to the bottom and select “Development Version” from the dropdown selector at the bottom of the page:
https://wordpress.org/plugins/wp-members/advanced/

Bleeding edge dev version is always available on github:
https://github.com/rocketgeek/wp-members-dev