Adobe has instructions for how to add a nonbreaking space in Illustrator CC here:
Here are the instructions for Adobe CC (in case the link above ever goes dead):
Prevent words from breaking You can prevent words from breaking at the end of lines—for example, proper names or words that could be misread when hyphenated. You can also keep multiple words or groups of words together—for example, clusters of initials and a last name. - Select the characters you want to prevent from breaking.
- Choose No Break from the Character panel menu.
Note: If you apply the No Break option to too many adjacent characters, the text may wrap in the middle of a word. However, if you apply the No Break option to more than a single line of text, none of the text will appear.
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I tested it by selecting two words that broke and choosing No Break from the Character panel menu. The words would not break between them anymore, so it works.