  Bound electron pairs (BEPs) with energy in the band gap are interesting
because they can participate in charge and spin transport in modern
topologically nontrivial materials. We address the problem of their stability
and study the radiative decay of the BEPs formed due to the negative reduced
effective mass in two-dimensional topological insulators. The decay time is
found to be rather large on the scale of the characteristic relaxation times of
the electron system and significantly dependent on the topological properties
and dispersion of the band states. In topological phase the decay time is much
longer than in the trivial one, and is estimated as $\sim$1~ns for the
HgTe/CdHgTe heterostructures. However, the longest decay time is in the
topological phase with nearly flat dispersion in the band extema.
