I recently had a recurrence and the following fixed it literally over night. I read that it often has to do with fungus, and given the location, the sores never heal as the lips are almost always moving. I have an anti-fungal shampoo that I use for my dandruff problem, and my experiment worked:
Clean the corners of your mouth, dry them.
Take a q tip and soak it in the anti-fungal shampoo (the medicated kind like Nizoral). Take a second qtip and soap it in in water. Rub the shampoo and water tips together to make them lather up as best you can, and gently wipe the corners of your mouth with the lather (mouth open to get it into the sores). Close your mouth, let the lather sit for 3-5 minutes, then rinse.
Do this before bed. In the morning there should be a significant improvement. I couldn't believe it, the cuts were closed up and I could yawn, eat, speak in peace. I hope this helps. Miriam