Topological protected wave engineering in artificially structured media is at the frontier of ongoing metamaterials research that is inspired by quantum mechanics. Acoustic analogues of electronic topological insulators have recently led to a wealth of new opportunities in manipulating sound propagation with strikingly unconventional acoustic edge modes immune to backscattering. Earlier fabrications of topological insulators are characterized by an unreconfigurable geometry and a very narrow frequency response, which severely hinders the exploration and design of useful devices. Here we establish topologically protected sound in reconfigurable phononic crystals that can be switched on and off simply by rotating its three-legged "atoms" without altering the lattice structure. In particular, we engineer robust phase delay defects that take advantage of the ultrabroadband reflection-free sound propagation. Such topological delay lines serve as a paradigm in compact acoustic devices, interconnects, and electroacoustic integrated circuits. This work is supported by National Key R&D Program of China (Grant No. 2017YFA0303702), NSFC (Grants No. 11674172, No. 11574148, and No. 11474162), Jiangsu Provincial NSF (Grant No. BK20160018), the Fundamental Research Funds for the Central Universities (Grant No. 020414380001), Nanjing University Innovation and Creative Program for Ph.D. candidates (Grant No. CXCY17-11), and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant No. YCX17_0020). J. C. acknowledges support from the European Research Council through the Starting Grant No. 714577 PHONOMETA and from the MINECO through a Ramón y Cajal grant (Grant No. RYC-2015-17156).