I use Mail.app with FastMail. Mostly, it just works.
However, when I start up Mail it never shows the Archive folder. The Archive button will move mail to it, but it's not there. The Goto mailbox menu item is greyed out for Archive in the Mailbox menu too. (cmd-2)
I can right-click on another folder, all of which show up, and choose "Get Account Info" then it scans all the folders, shows Archive which I double-click to open, and use that window, closing the original Mail window. All works fine and dandy. It's an annoying little dance I don't want to have to do.
Worth noting that once I've done the dance, then the cmd-2 short-cut works and the menu item above works fine.
In FastMail the Archive folder is configured to be displayed. It's set to Always Show.
This is on 10.9.2.
Using another mail client (Airmail, or Postbox) I didn't see this problem, but I like Mail.