Background and purpose: Eptinezumab reduced monthly migraine days more than placebo in the DELIVER study, a clinical trial with patients with difficult-to-treat migraine and prior preventive treatment failures. This post hoc analysis assesses the sustained response to eptinezumab at the population and patient level and evaluates the potential for response in initial non-responders. Methods: Adults with chronic or episodic migraine and two to four prior preventive treatment failures were randomized to eptinezumab 100 mg, 300 mg or placebo every 12 weeks. Primary outcomes in this post hoc analysis are the proportion of patients with ≥30%, ≥50% or ≥75% reduction in monthly migraine days (i.e., migraine responder rates [MRRs]) during weeks 1–12 and weeks 13–24 and across 4-week intervals. Secondary outcomes are maintenance and shifts in MRRs from weeks 1–12 to weeks 13–24. Results: Between weeks 1–12 and 13–24, ≥30% MRRs increased from 65.9% to 70.4% (100 mg) and from 71.0% to 74.5% (300 mg), versus 36.9% to 43.1% (placebo). The ≥50% and ≥75% MRRs were sustained or increased over the 24-week period. The largest increase in ≥30% MRRs occurred after the second infusion with eptinezumab. The percentage of initial non-responders (<30% MRRs during weeks 1–12) who experienced response (≥30% MRRs during weeks 13–24) to the second dose was 34.7% (100 mg) and 30.4% (300 mg) with eptinezumab versus 21.1% with placebo. Conclusion: Across MRR thresholds, most patients who responded to eptinezumab during weeks 1–12 maintained or improved response during weeks 13–24. More than one-third of initial non-responders became responders after their second infusion.