Supertoroidal light pulses, as space-time nonseparable electromagnetic waves, provided unique super-resolution topological properties including skyrmionic configurations, fractal-like singularities, and energy backflow in free space, which however do not survive upon propagation. Here we introduce the nondiffracting supertoroidal pulses (NDSTPs), propagation-robust skyrmionic and vortex-ring field that endure the singular configurations over arbitrary propagation distances. Intriguingly, the field structure of NDSTPs has a strong similarity with a von Kármán vortex street, a pattern of swirling vortices in fluid and gas dynamics, as the "singing" of suspended telephone lines in wind. NDSTPs allow the study of the propagation dynamics of electromagnetic skyrmionic fields and will be of interest as directed energy channels for information transfer applications.