I have zero addons installed, just to make that clear.
How I recreate the effect:
• turn on Action Bar 2 in Menu>Options>Action Bars>Action Bar 2
• In Edit Mode, right click Action Bar 2 and uncheck “Always Show Buttons”
• Fill the action bar up completely with abilities.
• Attempt to shift-drag abilities around, within that action bar
This causes the most recently dragged ability to not show on the action bar despite it actually being there.
Fix: check then uncheck the Always Show Buttons box, save.