  In recent years discrepancies have emerged in measurements of the present-day
rate of expansion of the universe $H_0$ and in estimates of the clustering of
matter $S_8$. Using the most recent cosmological observations we reexamine a
novel model proposed to address these tensions, in which cold dark matter
disintegrates into dark radiation. The disintegration process is controlled by
its rate $Q = \alpha \mathcal{H} \rho_{\rm ddm}$, where $\alpha$ is a
(constant) dimensionless parameter quantifying the strength of the
disintegration mechanism and $\mathcal{H}$ is the conformal Hubble rate in the
spatially flat Friedmann-Lema\^{i}tre-Robertson-Walker universe and $\rho_{\rm
ddm}$ is the energy density of the disintegrating cold dark matter. We
constrain this model with the latest 2018 Planck temperature and polarization
data, showing that there is no evidence for $\alpha \neq 0$ and that it cannot
solve the $H_0$ tension below $3\sigma$, clashing with the result obtained by
analyzing the Planck 2015 temperature data. We also investigate two possible
extensions of the model in which the dark energy equation-of-state parameter $w
\neq -1$. In this case it is possible to combine Planck data with the SH0ES
measurement, and we demonstrate that in both these models the $H_0$ tension is
resolved at the $1\sigma$ level, but the condition $w \neq -1$ exacerbates the
$S_8$ tension. We also demonstrate that the addition of intermediate-redshift
data (from the Pantheon supernova type Ia dataset and baryon acoustic
oscillations) weakens the effectiveness of all these models to address the
$H_0$ and $S_8$ tensions.
