If cats are trying to get on a bed that is at the same X,Z coordinates but nearby in the Y coordinate, they will stop near the bed and refuse to move or teleport unless you pull them with a lead or destroy the bed.  (You can also move them with water, but they will move right back to the spot when the water goes away.)

Recreating:

Create two platforms separated by 4 (i.e. 3 air blocks between them).

Place a bed on one platform (mine was on the upper level, but it works in either direction).

Bring some tamed cats to the other platform near the bed.

At this point they will cluster around the point below/above the bed, and if you walk away they will stay there.