Seyfert galaxies commonly host compact jets spanning 10-100 pc scales, but larger structures (KSRs) are resolved out in long baseline, aperture synthesis surveys. We report a new, short baseline Very Large Array (VLA) survey of a complete sample of Seyfert and LINER galaxies. Out of all of the surveyed radio-quiet sources, we find that 44% (19 / 43) show extended radio structures at least 1 kpc in total extent that do not match the morphology of the disk or its associated star-forming regions. The KSR Seyferts stand out by deviating significantly from the far-infrared - radio correlation for star-forming galaxies, and they are more likely to have a relatively luminous, compact radio source in the nucleus; these results argue that KSRs are powered by the AGN rather than starburst. KSRs probably originate from jet plasma that has been decelerated by interaction with the nuclear ISM. We demonstrate the jet loses virtually all of its power to the ISM within the inner kiloparsec to form the slow KSRs.