My Basenji had this problem on and off for years before I finally found a good solution. I actually just posted about it elsewhere in here so I'm going to attempt to quote it in here. Let's hope it works lol.
Copper, my oldest, has always had a sensitive stomach and would get diarrhea out of the blue all the time, so badly that he would have blood dripping from his rear. It freaked me out the first few times it happened! The vet always tried to prescribe an antibiotic but it never helped. The way I always got rid of it was to cook a pound of ground beef (rinsed), mix with a cup of cooked white rice, a cup of cottage cheese, and a cup of plain yogurt. You feed it for about 3-4 days (I always gave him about a cup and a half a day) and then start introducing their dry food back in. A friend on another forum gave me this concoction years ago and it worked perfectly for years.
Almost two years ago he got diarrhea and any time I would stop feeding the mixture it would come back. I finally consulted a holistic vet and she said I could continue feeding the mixture but needed to add some veggies to it for fiber, or I could change his dry food. She said to avoid chicken, wheat, soy, and corn. She also recommended feeding a probiotic/prebiotic several times a week in addition to two other supplements, Gastriplex and Moducare (both by Thorne). He's been on Taste of the Wild now, which is grain free (I buy the fish variety but they also have a bison/venison as well as a lamb), and and has had no problems. I'm very careful about the ingredients in the treats I give him now and have had NO diarrhea problems since changing his diet, which is absolutely wonderful!
Here are the links for what I use:
http://tinyurl.com/2adwtqn- 1 capsule 2x per day
http://tinyurl.com/276rn24 - 1 capsule 1x per day
http://tinyurl.com/2g47lsp - 1 capsule about 3x per week (I give it on Mondays, Wednesdays, and Fridays)