Tink, I've been dealing with skin allergies with my yorkie, Hobbs, for over a year now. I've finally gotten it under control. I would suggest eliminating not only corn, but also other sources of allergies in dogs. I would switch to an exotic protein source...one that Moses has never been exposed to so you know he hasn't built up a sensitivity to it. Since most foods contain chicken and rice, it's best to switch him to something that doesn't contain chicken or rice since he's probably been exposed to these and has possibly built up a sensitivity to them. I suggest duck or fish based foods with potatoes as the carb instead of rice. Also, eliminating gleuten (Wheat, Barley, Rye), corn, dairy and soy. I found that Barley is a killer for Hobbs. So many treats and foods have barley and wheat in them. I would highly suggest switching to food and treats that do not.
My favorite allergy foods for dogs are the Natural Balance formulas......Duck & Potato or Sweet Potato & Fish are both great and have really helped Hobbs' skin. He was losing patches of hair all around my house too. But now he's 100% better!!! You also may want to add some Omega Fatty Acids to his food. I suggest Salmon Oil.
Here's the world's BEST website for people are who struggling with allergies in their dogs. It's helped me tremendously! It takes awhile to digest, but it's WELL worth the time it takes to read it!
http://dogtorj.tripod.com/id5.html
If you have any questions, feel free to PM me! When it comes to dog skin allergies, I've been there, done that!!!!!!!!
Oh and back to your original question, it will take a good month to see any difference if the new food you've gotten him does do the trick.