Text is appearing outside of text box. Is this a technical limitation of Illustrator?

Hello,

I'm working on a project involving a lot of text inside of a large text box. The text is very small and contains several thousands of words. With my hyphenation and justification setting, some parts of the text--the leftmost portion of the text--spills out of the text box.

Here is a screenshot capturing my problem:

Here it is zoomed out:

How do I prevent this from happening? All text in the box must stay within the boundary box.

Thank you.