Hi NoodleDriver,
Not that I know of, there shouldn't be a limit number of subparts.
Your subparts are mislabeled in the schematic.svg; i.e. In your .fzp the subpart is labeled "id="subpart5"". In your schematic.svg your subpart is labeled "id="subpart5_1_". The underscore 1 underscore could have been generated automatically if you had duplicate ID names.
You can just open the schematic.svg in a text/xml edition and delete the underscore 1 underscore from the three layer IDs and re-save.