Mr. Rewrite's newspaper must have its own style for nonprofit vs. non-profit, as it uses non-profit consistently. This lead from an AP article is an example.
Consistency is Mr. Rewrite's No. 1 usage goal, so this is OK with him. But he needs to point out to impressionable journalism students, who ignore the daily paper at their peril, that AP style is nonprofit. See below for an image grab from his mobile stylebook. That AP article has it as nonprofit on other sites, by the way.
The AP Stylebook recently added an entry codifying nonprofit, but Mr. Rewrite has demanded it for years because the stylebook uses that form within other entries. The entry on non- should cover the term but has some ambiguity. How did Mr. Rewrite know this? He has a soulmate-strong relationship with his reference books.
When in doubt, look it up. That's how Mr. Rewrite avoids missing his wedding anniversary.