It looks like renderRegions is only called if _polygonBatch is null, a byproduct of sending false to the creation of the SkeletonSprite, (or ultimately SkeletonAnimation).
However, _polygonBatch attempts to act as a batch for all subsequent Spine animation children. This is a problem if you've stopped the current animation, but the siblings have not stopped.
Another issue is that PolygonBatch clears out its vertex data on flush(). The first reason is because of its use for multiple skeletonanimations, and the second possible cause is because the transformation matrix is flattened (at least when rendering multiple skeletons).
I would probably try the following approach: derive 2 new classes. One from SkeletonAnimation and the other from PolygonBatch.
The new SkeletonAnimation would include the Juggler modification I suggested previously combined with some sort of 'animating' boolean that would get set to false on stop (or lookup some isAnimating value). It would also include an override for the render() method that would cache all vertices into the new PolygonBatch class, but only for this particular sprite.
The new PolygonBatch override class would not discard the vertices on Flush(), but would have a manual 'clear()' method that the new SkeletonAnimation class would call when the vertices are marked dirty (updated).
In any event, try the polygon batching mode first before to see how it affects performance and all you should really need is a boolean set to true.
