Designer work is stored in your browser from session to session. If you use a different browser (or clear out your browser), you will not see your old projects.
Each time you Publish or Export, a file is written to to your Downloads directory. That file has the .stardogdesigner extension.
In Designer, there is an arrow next to the New button. There you can choose "Import Project" and load a saved .stardogdesigner file.
The model (but not the mapping) is also saved to the database you published the model to. You can pull that back into designer with the plus button:
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