  The celestial reference frame is realized by absolute positions of
extragalactic sources that are assumed to be fixed in the space. The fixing of
the axes is one of the crucial points for the International Celestial Reference
System (ICRS) concept. However, due to various effects such as its intrinsic
activity, the apparent position of the extragalactic sources may vary with
time, resulting in a time-dependent deviation of the frame axes that are
defined by the positions of these sources. We aim to evaluate the axis
stability of the third realization of the International Celestial Reference
Frame (ICRF3). We first derive the extragalactic source position time series
from observations of very long baseline interferometry (VLBI) at the dual
$S/X$-band (2.3/8.4~GHz) between August 1979 and December 2020. We measured the
stability of the ICRF3 axes in terms of the drift and scatter around the mean:
(i) we estimate the global spin of the ICRF3 axes based on the apparent proper
motion (slope of the position time series) of the ICRF3 defining sources; (ii)
we also construct the yearly representations of the ICRF3 through annually
averaged positions of the ICRF3 defining sources and estimate the dispersion in
the axis orientation of these yearly frames. The global spin is no higher than
$\mathrm{0.8\,\mu as\,yr^{-1}}$ for each ICRF3 axis with an uncertainty of
$\mathrm{0.3\,\mu as\,yr^{-1}}$, corresponding to an accumulated deformation
smaller than $\mathrm{30\,\mu as}$ for the celestial frame axes during
1979.6--2021.0. The axis orientation of the yearly celestial frame becomes more
stable as time elapses, with a standard deviation of 10--20$\mathrm{\,\mu as}$
for each axis. The axes of the ICRF3 are stable at approximately
10--20~$\mathrm{\mu as}$ from 1979.6--2021.0 and the axis stability does not
degrade after the adoption of the ICRF3.
