Taking into consideration what you have done and the fact that different diets were tried.....Since the diarrhea clears up on antibiotics, it seems to me the problem is a bacterial one. The routine fecal exams done at your vet office would not be able to diagnose this. A sample of the stool needs to be sent to a lab, and I would suggest a couple of tests: (you didn't mention that any of these were done, so I'm assuming they were not)

1- a fecal culture. This can help diagnose nasty bugs like Campylobacter that can cause diarrhea
2-a fecal pathogen test (this is called many things by different labs) This usually tests for Giardia and Clostridium enterotoxin. These are also bugs that cause diarrhea. Clostridium is found in many dog's stools, but the strain that produces the enterotoxin will cause chronic diarrhea in many dogs, and can contaminate the environment.

These tests are not inexpensive, so be prepared to have this cost more than a regular stool sample check. It may be worth it if you can find the cause of your dog's problem.

The antibiotics your dog was on will treat many of these. However, the length of treatment can be longer than what most vets prescribe. I will usually treat Clostridium for at least 4 weeks. Many times improvement is not seen for a couple of weeks into treatment. Sometimes a combination of 2 antibiotics (like flagyl and amoxicillin) will work better than just one alone.

Also, I always deworm with Panacur (fenbendazole) even if the stool samples come back negative for worms. Whipworms are very hard to find in stool samples, and they certainly will cause diarrhea.

Another possibility is to have your vet check your dog's pancreas funtion. If the pancreas isn't producing the proper digestive enzymes, the dog will have diarrhea all the time. This is a bit rarer, and generally the dog will be losing weight and having other symptoms of a problem.

That is what I would do if this dog were my patient, I hope this helps.