Does this sentence make sense.
Students may not still have a sweet tooth by Thanksgiving.
OR
Would it be more correct to leave the still out?
I'd leave "still" out.
Or reword it -- Students still may not . . .
OR how about
Students may indulge in their sweet tooth before Thanksgiving.
It's o.k., but doesn't have the same meaning as your original sentence.
The sentence "Students may not still have a sweet tooth by Thanksgiving" is grammatically correct and makes sense. However, whether or not to include the word "still" depends on the intended meaning you want to convey.
If you include "still," it suggests that students previously had a sweet tooth, but it is uncertain whether they still have it by Thanksgiving. In this case, there is an implication that their preferences may have changed over time.
If you leave out "still," it implies that students may not have a sweet tooth at all by Thanksgiving, without explicitly referencing their previous preferences.
Both versions are valid, but they convey slightly different meanings. It would be more a matter of what you want to emphasize or the context in which you are using the sentence.