I don't have that problem. Perhaps you have to set "Show my windows and tabs from last time" in "Settings" > "Genera" > "When Firefox starts".

My pinned tabs are still there, when I close the window as well as when I exit Firefox.

Edit: This doesn't work, if you have multiple windows and close that one with the pinned tabs before another one.

But there is still the possibility, to set mutliple pages as start page. Just open the pages you want to have opened on start, then go to the settings and choose "use current pages".

Thanks GG,

Not quite what I was after, the problem still occurs (although I do not have this problem using App Tabs in FF4 on Windows). My current situation is:

I have the tabs I want to automatically open every time I start a new session in FF4 pinned. In my preferences, I have the "Show my windows and tabs from the last time" checked, and my homepage is set to Google. If I click the 'x' button in the top left corner and then open FF4 from the dock, a window will open with my App Tabs still there and still pinned, and Google open in a tab (unpinned). But, if I click the 'x' in the top-left corner and then quit FF4 (i.e., from the Firefox drop-down menu, 'command-Q') and then reopen from the dock, a window will open with only Google open in a tab. However, if I quite FF4 from the drop-down menu (or 'command-Q') while the current window is open (App Tab's still pinned, i.e., I haven't clicked the 'x' button in the top-left corner), then when I reopen from the dock my App Tabs are still pinned and another tab with Google in it will open.

This seems to be the only solution, albeit a rather complex one, to the problem I have found. It would be much easier if the App Tabs would be permanent, no matter which way I close/quit FF4.