Why is bold italic and italic text not applied for some fonts when applying a text style file on a Dynamic Content XML file?
Style mapping can work only with font types already available in the system. If an Adobe® Illustrator® file is saved after applying the Style mapping in a state that bold and italic types are unavailable, the document remembers it.
Then, even if you open the document with all the font types available, if there is no need of XML refresh, the text stays without bold and italic. Refreshing the XML link by clicking Synchronize or re-linking particular element re-applies the Style mapping what fixes the issue.
It's always better to have all necessary font types available during all stages of preparing dynamic document.