Hi guys as experienced the same problem these last days with my yahoo conversation history on my iPhone, ipad and on my android phone I tried all the day to find a solution. So the solution that I found is:
1. Login in your yahoo mail from the browser, not from the application.
2. Open the "Options" folder
3. Select "Go back to classic mail"
4. Select "Conversation" folder
I know it's not that easy as it was, but I guess it's the only way till yahoo fix the problem.