Looking again at the short video, I think it is a focus problem. Are you sure that you are not exceeding the cameras ability to close focus? Check the manual and in the specifications, what is the closest focus distance?
In a still camera, including my A77 which can take video, if you get too close to the subject, it simply cannot focus. It doesn't jump around like your camera does. This type of problem on a still camera depends on the lens used. That is why we use macro lenses and can get as close as 1 to 1 magnification.
Video cameras, and I assume you have a fixed lens, are very unlikely to have a lens that can get as close as a Macro lens, in fact I doubt that you can get any closer than you are trying to get in your short video. In the part where the steadyshot is off, it is already jumping around with no help from the stabilization. I cannot explain that without more information.
When the steadyshot is in standard mode you get very close but the flowers and pot are out of focus. The steadyshot is helping, but the lens cannot get focus.
In the Active mode you seem to get even closer without, the jumping around, but again the flowers and pot are out of focus. Active Mode may be a stronger stabilization than standard mode, allowing you to get closer.
In conclusion, I think you are trying to get too close. As you get inside the minimum focusing distance of your cameras lens you will never achieve focus, not with any Video camera that I know of, except possibly one with interchangeable lenses.