This question is incomplete. You need more context to learn about the motion.
I will show you some cases for which the vertical distance does not change at constant rate:
1) If object A is moving on a path that is parallel to an arbitrary line, the distance between the object A and the line will not change.
2) If object A is moving at the same rate than it is doind object B, the distance between object A and object B will not change.
Without more information from you this is what I can do and I think it is useful.