The short answer: A refused document can usually be fixed and resubmitted. The recurring causes are well known: a missing or wrong-authority apostille, a power of attorney written in broad general wording, a translation the notary does not accept as certified, or a name spelled differently across your documents. A short, specific conversation with that notary about their exact objection saves weeks of guessing.
Ukrainian notaries carry personal liability for the acts they certify, so they screen foreign documents strictly. A rejection is a signal about one specific defect, and once that defect is identified, the correction is normally a targeted redo of one step — a re-drafted text, an added apostille, a corrected translation — rather than the whole chain.