The Primary Classification field is a formula field on the Donation record that is populated based on the Primary Classification of the donor at the time the gift is received. This means that if the donor does not have a Primary Classification on their Contact record when they make the gift, it will also be blank on the Donation record.
If you are looking at gift where the Contact record does have a Primary Classification, check to the Contact history to see if there was a duplicate merge at some point in the past. If there was a duplicate record, and that Contact was the original donor on the gift, the Primary Classification field may not have been populated on the duplicate Contact record. This is why the classification was not populated on the donation.
In order to avoid this in the future, admins can check the Primary Classification field for donations associated with duplicate contacts before or after they are merged. You could also set up a report for your key groups (like Board Members) that returns all donations with a blank Primary Classification associated with donors of that type. If you review those results periodically, or after any large-scale duplicate management activities, it should take away the hassle of dealing with it when you're running reports on the Primary Classification field.