Do the following, just tested, steps:

1. Add the parameter -console to Launch Settings of Portal 2
2. Launch Portal 2 (developer console should be already there)
3. Write and execute in console: bind f11 toggleconsole
4. Test that pressing F11 toggle the console
5. Now exit Portal 2 and relaunch it. Everything should work as expected.

Do the following, just tested, steps:

1. Add the parameter -console to Launch Settings of Portal 2.
2. Launch Portal 2 (developer console should be already there).
3. Write and execute in console: bind f11 toggleconsole
4. Test that pressing F11 toggles the console.
5. Now exit Portal 2 and relaunch it. Everything should work as expected.