Labels (and their text) of inner graphs are exported to SVG documents:GraphML file. Corresponding SVG document.
If text in your inner graphs is not displayed in exported SVG documents, I guess the zoom factor of the inner graphs is below yEd's "Paint Details Threshold" (see "File" -> "Preferences", tab "Display"). If you set "Paint Details Threshold" to "0", text is never omitted and you should get the desired result when exporting to SVG.