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 $Gamma = alpha mathcal{H}$, 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. We constrain this model with the latest 2018 Planck temperature and polarization data, showing that there is no evidence for $alpha eq 0$ and that it cannot solve the $H_0$ tension below $3sigma$, 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 $w eq -1$. 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 $1sigma$ level, but the condition $w eq -1$ 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.
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