besides what Elina said it also means being strong in the face of problems. basically your lip doesn't quiver when there are a lot of problems in front of you.

I don't know the song, but keeping a stiff upper lip means hiding your true feelings or acting overly polite and formal. At least that's how I've always understood it :)

Don't loose your courage! = to keep a Stiff upper lip!

Check it here: http://en.wikipedia.org/wiki/Stiff_upper_lip

I always keep a stiff upper lip, in spite of what i am sufferring.