Upgraded to WordPress 3.7.1, and the problem is solved.
I followed the discussion on what exactly caused this. The WP core development team implemented a small but critical change that could potentially affect numerous plugins, and it was not a problem with Plugin Organizer at all.
This plugin is a real gem: the ability to organize the dozens of plugins I have is very helpful, as well as the plugin filter to selective load them only when needed. I’m glad the issue is functionally solved, although the real cause in the core still needs to be addressed, it seems.
Anyway, I wanted to express my appreciation for Plugin Organizer, really nice work, thank you.