Mission Ranks don't update on the Mission Select screen.
I'm working though getting A++ on all levels and I'm currently on The Darkside of Mars. I got an A in Gatecrasher as seen here but here's what it looked like when I go back to the Mission Select. the same goes for Limbo, here and here.
It looks like I'm not the only one that encountered the bug, someone posted about it over on the subreddit.
Just wondering if RL knows about this bug. My Ranks for each level is updated correctly though when I view my Inner Beast in the Global leaderboards. Hopefully it doesn't mess with any of the A/A++ achievements.