  Conflicting values of the hypertriton ($_{\Lambda}^{3}$H) lifetime were
extracted in recent relativistic heavy-ion collision experiments. The ALICE
Collaboration's reported $_{\Lambda}^{3}$H lifetime $\tau(_{\Lambda}^{3}$H) is
compatible within measurement uncertainties with the free $\Lambda$ lifetime
$\tau_{\Lambda}$, as naively expected for a loosely bound $\Lambda$ hyperon in
$_{\Lambda}^{3}$H, whereas STAR's reported range of $\tau(_{\Lambda}^{3}$H)
values is considerably shorter: $\tau_{\rm
STAR}(_{\Lambda}^{3}$H)$\sim$(0.4-0.7)$\tau_{\Lambda}$. This $_{\Lambda}^{3}$H
lifetime puzzle is revisited theoretically using $_{\Lambda}^{3}$H three-body
wavefunctions generated in a chiral effective field theory approach to
calculate the decay rate $\Gamma(_{\Lambda}^{3}$H$\,\to ^3$He$\,+\pi^-$).
Significant but opposing contributions arise from $\Sigma NN$ admixtures in
$_{\Lambda}^{3}$H and from $\pi^-$-$^3$He final-state interaction. Evaluating
the inclusive $\pi^-$ decay rate $\Gamma_{\pi^-}(_{\Lambda}^{3}$H) via a
branching ratio $\Gamma(_{\Lambda}^{3}$H$\,\to
^{3}$He+$\pi^-)/\Gamma_{\pi^-}(_{\Lambda}^{3}$H) determined in helium
bubble-chamber experiments, and adding $\Gamma_{\pi^0}(_{\Lambda}^{3}$H)
through the $\Delta I=\frac{1}{2}$ rule, we derive $\tau(_{\Lambda}^{3}$H)
assuming several different values of the $\Lambda$ separation energy
$B_{\Lambda}(_{\Lambda}^{3}$H). It is concluded that each of ALICE and STAR
reported $\tau(_{\Lambda}^{3}$H) intervals implies its own constraint on
$B_{\Lambda}(_{\Lambda}^{3}$H): $B_{\Lambda}\lesssim 0.1$ MeV for ALICE,
$B_{\Lambda}\gtrsim 0.2$ MeV for STAR.
