First off how old is he? If he isn't very old it takes a while for their little bladders to be able to go for very long. Somtimes just when you think you have them broke they have an accident,
it's all part of the puppy stage just try and be patient and don't give up he will get it just like a light comes on and they get it. The leash is a good way to break them I know you said you don't want to do that but it works.