Some ideas...not sure if you've tried these already.
1) Rule out/experiment to determine if this is possible Food Allergies:
You mentioned switching dog food to one that is wheat and corn free. One of my female pointer dogs racked up numerous vet bills where they did skin scrapings, I tried benadryl, vet put her on repeated courses of antibiotics and prednisone and none of these resolved her ongoing skin issues. So I began trying different more expensive dog foods that were limited ingredient diets. When I tried her on California Naturals Lamb and Rice; it finally put a stop to her skin issues. It turned out that she was sensitive to any dog food that contained chicken.
After I had her on the CA Nats Lamb +Rice, I figured I'd try their CA Naturals Chicken and Rice. Within a matter of days on the Chicken food, my dog's skin issues promptly returned. When I put her back on either CA Naturals Lamb and Rice or CA Naturals Herring and Sweet Potato, her skin clears up and itching stops. For some reason for that particular dog, any food that contains chicken meat, chicken meal/byproducts, or similar, sends my dog right back into the itching frenzy.
There are other brands besides the one I mentioned that are limited ingredient diets; I just tried that brand of food because it is sold at a pet supply store that is close to my home. When my dog was having skin issues, I went online and found articles about Food Allergies for Dogs. Some of the articles suggest homemade elmination diets to help determine what specific allergen is bothering the dog.
2) Has Vet Ruled Out a Thyroid Issue or Done Recent Bloodwork?
Has your vet run a blood test recently on your border collie and if so, did they check the dog's thyroid levels? A Senior Blood Panel done on a dog could be very helpful to determine if there is something going on with the dog like Hypothyroid, Cushings, or other endocrine issue that can cause recurrent skin issues. If blood test found that the dog has low thyroid, the Rx medicine for low thyroid is inexpensive.
3) I did a google search for "Skin Conditions affecting Border Collies" and found this Australian purebred dog forum where back in 2007-2008, they had a 3 page online discussion on where several Border Collie breeders and owners discussed what they did to resolve recurring skin conditions on border collies. It was really interesting because they talked about specific environmental, health conditions, and other indoor/oudoor exposure things that can trigger skin issues in BCs and what they did to fix the issue with their border collies. The topic was part of their archive; so they aren't accepting new comments to that particular topic, but, I learned some things by reading it and felt that it might give you some helpful insights. The link is:
http://www.*********.com.au/topic/122048-border-collie-skin-problems/
Wishing the best to you and your border collie.
You need to look into this being a Yeast Infection.....If that's the case, antibiotics will make it worse......Please google Nzymes.Com and read everything you can from their site......I feel it will help you and your dog out....Karla
P.S. What food is it and for how long?
I have actually tried that. I've also tried an all natural remedy that hasn't worked either.
Have you tried Benedryl? One of my girls get's sores that weep and bleed and scab over, that she scratches to death, and it's attributed to seasonal allergies.
My vet recommended I try Benedryl, and I've not looked back. I start in September, and she takes it through November, then again in March through May (those are all my girl's allergy seasons).
Check with your vet on the dose, but it's gotta be worth a shot, right? Surely it's cheaper than all the other stuff you've been trying.