  The gas depletion factor $\gamma(z)$, i.e., the average ratio of the gas mass
fraction to the cosmic mean baryon fraction of galaxy clusters, plays a very
important role in the cosmological application of the gas mass fraction
measurements. In this paper, using the newest catalog of 182 galaxy clusters
detected by the Atacama Cosmology Telescope (ACT) Polarization experiment, we
investigate the possible redshift evolution of $\gamma(z)$ through a new
cosmology-independent method. The method is based on non-parametric
reconstruction using the measurements of Hubble parameters from cosmic
chronometers. Unlike hydrodynamical simulations suggesting constant depletion
factor, our results reveal the trend of $\gamma(z)$ decreasing with redshift.
This result is supported by a parametric model fit as well as by calculations
on the reduced ACTPol sample and on the alternative sample of 91 SZ clusters
reported earlier in ACT compilation. Discussion of possible systematic effects
leaves an open question about validity of the empirical relation
$M_{tot}$-$f_{gas}$ obtained on very close clusters. These results might pave
the way to explore the hot gas fraction within large radii of galaxy clusters
as well as its possible evolution with redshift, which should be studied
further on larger galaxy cluster samples in the upcoming X-ray/SZ cluster
surveys.
