So many possible reasons...
Can you post a screenshot?
Does the text that doesn't print show if you switch to Overprint Preview?
You sent a private message indicating the text does not show in overprint preview. If that is true there are two likely scenarios: It's on a layer set to non-printing or the frame is set to non-printing, or there is a blend mode involved in putting the text against a background. We need to see, at the very least, a screen shot of the page and the layers panel.