If you ignore the ground and the performer (as they seem to be causing you trouble), as the objects fall, they will not tumble without outside forces (like air buffetting). Because they spin around a stable axis, they will remain spinning around that axis.

In the system seen, the air resistance is slowing them down while gravity pulls them down, which are both countered by the repeated kicks. Within that system, the objects spin instead of tumble due to gyroscopic effects that come from rotating bodies around a stable axis.

Saying it isn't stable due to the forces imposed by the performer is like saying a box on the ground is not stable because the ground is pushing it up. All systems have various forces working on them, and defining stability is about whether the system remains as is with the same forces, or if it changes under no change of forces.

While we could be pedantic and say there is nothing stable in the universe due to entropy, that is a very unhelpful and non-insightful response~

While, it seems obvious to me that OP wasn't asking why the objects were just floating there, defying gravity as if OP couldn't see the performer, apparently that wasn't globally obvious.