I had raised an issue with the sozi team regarding its interop with svg files created using yed.
The issue and their response is available at https://github.com/senshu/Sozi/issues/295#issuecomment-209060648
I am copying it here for reference, please look into the issue and fix it if possible.
I wish there was some way for the tool to remember the zoom level of each frame and its position with respect to a key element in the frame.
This is exactly how Sozi works. If you reopen the same SVG, Sozi should remember the geometry of all frames even if some elements have moved. However, it requires that the key elements are still there and that they have the same identifier.
If I understand your situation correctly, it seems that YEd does not assign the same ids to the SVG elements when you reexport your diagram.
I have tried yEd and actually it does not assign ids to the generated SVG elements.
There is no easy way for Sozi to keep track of key elements