Actually this is very possible and its fairly easy to do. Once your animated loop is in cta. you can turn it into a smart prop. In this case you may need tp ad ad an additional 1 frame sprite, depicting the stopped state.
Basically you animate the prop the way you want in the stage and use the collect clip function to export animations, sprite switching events, and so on. These exported animation can then be brought back and applied to the prop so that you can control it with the action menu. This way you can literally make it so you can control all sorts of things in that prop, such as whether it loops for ever, whether it stops, or changes angles etc.
In your case all you need to do is create two action menu items, one that tells it to cycle, and one that tell it to stop.
If you use Billy check out the Icarus Mod Pack. Icaru's wings have various states that you can control with the right click menu. such as expand, contact, fly etc. Its the same concept