What Is the Smallest Declination a Star Can Have so That It Never Sets?
The smallest declination angle that a star can have so that it never sets on the horizon would be a positive fifty-nine degrees. This should make it so that you can see the star whether it is day or night.
1 Additional Answer
It depends on what latitude you're viewing the star from. The lowest declination a star can have, and still be visible at certain latitude, is calculated as 90 degrees minus the latitude.