Then put an empty keyframe just before the Move_x keyframe, and put a Play action into it.

Creating Continuity. 

When the playhead reaches the Move_x keyframe, it jumps to the previous frame and the content is displayed in Flash. As soon as the new content is displayed, Move_x works its magic again, everything is reconfigured and the updated content displayed, and so on through the loop.
If you need to apply this effect to several movie clips, a practical approach would be to create a ‘shaker’ clip to shake any clip into which it is inserted.