  Long-time existence of topologically nontrivial configurations of quantum
vortices in the form of torus knots and links in trapped Bose-Einstein
condensates is demonstrated numerically within the three-dimensional
Gross-Pitaevskii equation with external anisotropic parabolic potential. We
find out parametric domains near the trap anisotropy -- axial over planar
frequency trapping ratio $\lambda\approx 1.5-1.6$ where the lifetime of such
quasi-stationary rotating vortex structures is many hundreds of typical
rotation times. This suggests the potential experimental observability of the
structures. We quantify the relevant lifetimes as a function of the model
parameters (e.g. $\lambda$) and initial condition parameters of the knot
profile.
