Here are some things you can try (in no particular order);
Select all the type and open it in story editor (edit> Story editor) there should only be one paragraph.
With the type still selected, check the leading, size, baseline shift, etc. if a setting is blank, throw a number in it.
Go to paragraph styles, clear all overrides.
Give the text wrap offset a negative number.
Make a new layer and move your type to it.
Fill the paths with a color, fill the text box with a color (just to show any possible issues, like stray paths).
Select and delete the text a little above and below the gaps, is the gap still there?
Open and re-save your paths in Illustrator, save as .ai or .pdf (not .eps).