A delivery device for percutaneously deploying a stented prosthetic heart valve. The device includes a delivery capsule and a recapture sheath. The capsule is configured to compressively retain the prosthesis. The recapture sheath includes a funnel segment having a plurality of circumferentially spaced runners and a polymer overlay. The runners are attached to a shaft and terminate at a distal tip. The overlay surrounds the runners, and is bonded to the shaft but not to at least the tips. The funnel segment is transitionable from a normal condition to an expanded condition forming a funnel shape with a distally increasing diameter, and self-transitionable back toward the normal condition. The funnel segment facilitates sliding of the capsule over a partially deployed region of the prosthesis as part of a recapturing operation. The runners provide columnar strength, with the overlay controlling a shape of the funnel segment.