The phrase "to hold on" means to continue or persist in an action, belief, or course of conduct despite difficulties or opposition. It implies perseverance and determination in the face of adversity.
These are the investors who don't hold on stocks for more than a year. (getoutofdebt.com)
Instead of holding on to how they wish things were, they embrace how things are by appreciating those things that are going right in their lives. (inc.com)