  We present a theoretical study of resonance lifetimes in a two-component
three-body system, specifically examining the decay of three-body resonances
into a deep dimer and an unbound particle. Utilising the Gaussian expansion
method together with the complex scaling method, we obtain the widths of these
resonances from first principles. We focus on mass ratios in the typical range
for mixtures of ultracold atoms and reveal an intriguing dependence of the
resonance widths on the mass ratio: as the mass ratio increases, the widths
exhibit oscillations on top of an overall decreasing trend. In particular, for
some mass ratios the resonance width vanishes, implying that the resonance
becomes in fact stable. Notably, near the mass ratio for Caesium-Lithium
mixtures, we obtain nearly vanishing widths of the resonances which validates
to treat them in the bound-state approximation. In addition, we perform our
analysis of the resonance widths in both one and three dimensions and find a
qualitatively similar dependence on the mass ratio.
