For shadow-casting spot lights, decrease the Cone Angle.
For shadow-casting directional lights, turn off Use Auto Focus; turn on Use Light Position, and set Width Focus so all objects that you want to cast shadows do indeed cast shadows for all frames of the animation.
To determine the Width Focus value, select Panels > Look Through Selected, and zoom the view in or out until all shadow casting objects are visible. Note the width of the view and use this value for Width Focus.
For all light types, you can do one of the following:
- Turn off Use Light Position (for directional lights only), turn on Use Auto Focus for the light, and turn off Casts Shadows for any objects (especially large objects) in the scene that do not need to cast shadows (they can still receive shadows).
- Increase Filter Size (to the lowest value that produces acceptable results) for the shadow casting light (this makes shadow edges softer).
- Increase Resolution (to the lowest value that produces acceptable results) for the shadow casting light.