My '54 3100 had exactly the same problem. After a complete brake rebuild (my first and it turned out fine - which means any goof can do it) the problem was solved. Everything was rebuilt - wheel cylinders, new shoes, new springs. Good luck!
If you are interested in working on it yourself, I'd recommend a Haynes manual. You can pick one up at Barnes & Noble. Mine is for mid-seventies to late eighties Chevy trucks. The brakes on my '54 were exactly like the ones in the book. I looked at the pictures, followed the instructions, and got it done.
