What is a sub-plot?
When it rains it pours, right? When you have a huge project due at work on Friday, your kids get sick, your car breaks down and your computer dies for no apparent reason. The same thing should happen to your protagonist.
Just because your protagonists must do everything in their power to achieve their goals, it doesn’t mean that it is the only thing they must do. Nothing happens in isolation. That is where the sub-plot comes in.