Some satellites do not have AOS/LOS events for all points on the globe. However they are may be visible and not necessarily stationary in the sky. The SIRIUS constellation as well as geostationary satellites with poor station keeping can fall into this category over North America.
Perhaps the next certain number of hours or orbits would be used for computing these as in ground track case.
This would be somewhat involved as it would involve changes to the pass generation routines and pass plotting routines.