What you're seeing is the known issue with S3D not handling minute errors and inconsistencies in the model mesh correctly.
A first try at resolving the issue would be to upgrade to the new release v3.10, which according to the changelog has coding changes specifically to address the type of issue you are experiencing.
If upgrading doesn't improve the slicing when rotated, try altering the layer thickness by 0.001 mm, either up or down, and see if that resolves the slicing issues.
A third way to address this would be to submit your .stl file to the cloud model repair service: https://netfabb.azurewebsites.net/
Import the fixed version and try slicing again.