These two features interact poorly when you choose to display the center mark of a radial dimension. Radial dimensions have two parameters which control the display of a center mark and its size.
When you use these to display the center mark you will need to expand the annotation crop region so that the center mark is visible, otherwise the dimension will not be visible at all.
As pictured here.
If you need to crop a view and see the radial dimension when its center mark is well outside the cropped view you need to use a dimension style that does not display the center mark. Just create a new dimension style and uncheck those options. Use this style in any view that you need to crop but still see the radial dimension. You also need to adjust the dimension line length so it does not extend beyond the Annotation Crop Boundary.
Keep in mind that if you want to see the Center Mark in a coarser scale view, just use the original dimension style.