See the anchor comment at O.04.489 on root duk-/deuk-‘continue’
This adjective adeukḗs occurs in contexts referring to an interrupted sequence. Nausicaa is concerned that the Phaeacians may say something, as expressed by the noun phēmis ‘something said’, that is adeukḗs for her reputation. Good reputation is conceived as a steady stream of speech, the interruption of which threatens to produce a bad reputation.