The "ball of doubt" is sometimes called the "labyrinth of doubt". It refers to those times in training where the student gets lost in doubt and can despair of ever really grasping the art he/she is studying. Sometimes this can lead to the student quitting, "this is too hard, I give up" or "none of this stuff works anyway so it's not worth the effort". And this of course does not have to apply to only internal martial arts. It can be anything a person is trying to master, or at least acquire some skill at doing. It could be acting or knitting or any of the thousands of things humans try to do.
The ball of doubt however is not a bad thing. It signals an opportunity and it usually only happens after you have acquired a certain skill level. Of course when we walk away from something early in our efforts we may just be recognizing that it does not really interest us or that it is not something we are really suited too. The ball of doubt is different. It may happen many years into a person's practice and after a great deal of daily effort has been expended. In my case it happened while I was laying on a bed in a hotel in Shanxi China. After many years of practice I felt the great ball of doubt weighing on me. I thought that I might never get Master Li's expression of Xingyi. I had gotten many things but only part of the real internal development I felt was so essential and that I clearly saw in Song Zhiyong.
Traditionally, they say that when you experience the ball of doubt it signals the time to go to your teacher and he/she will point out what you need to do in order to reach the next level. (I think there is another thing that must happen and that is to resolve to continue anyway. In my case I thought "well, maybe this is a good as i will ever get but I might as well keep going forward because no matter what I do time will pass anyway".) Fortunately the next day my elder school brother Song Zhiyong went into a deeper explanation and demonstration of methods of training that set me on the right path. I was able to identify those things I needed to do in order to further develop my Xingyi.
The ball of doubt gives you an opportunity to identify what is wrong and what you can do to improve and grow. Embrace it because without that "ball" it is very easy to just continue on thinking that you are really good. You know all the forms! They look good! You have success in fighting or tui shou! Everything is great and you have mastered the art! But all you really have is the "skin of the tiger".