Starcraft 2: can you permanently display the frames-per-second?

You can do that by configuring the game using the battle.net client, check the "Additional command line argument" checkbox.

And in the input that appears, you can enter -showfps=1.

If you don't launch the game using the battle.net client, you can try editing the properties of the shortcut you use to launch the game by adding that argument after the path of the game.

I tested it yesterday, it seems to work. The only time the info disappears is when you are on the loading screen, where there are Kerrigan, Raynor and Artanis's faces, and it reappears on the next screen.

You can make it disappear anytime by hitting ctrl+alt+F again.