When using the center point slot tool in the sketch environment, the center point of the slot does not actually constrain to the selected center point. Most other sketch entities allow automatic constraining (like lines and circles, auto-constrained to the points picked).
The center point slot should follow this behavior. The overall slot seems to also have problems constraining to points picked. It seems the construction line can be snapped to the opposite tangent of the circle if the geometry moves correctly.
Of course you can always use the constraint tools in the sketch panel or drag-drop geometry to re-constrain. But you shouldn't have to if you've already picked the points where you want your geometry constrained. I've gotten to the point where I regularly draw slots where I don't want them and then drag them into location because it's less work that way.
The center to center slot seems to constrain fine, like most of the other geometry in Fusion 360.