Some Google Home Mini units seem to be suffering from an issue when they play music. Specifically, some users are reporting that the music playback action results in the Google Home Mini crashing and initiating a reboot. At present, Google does seem to be aware of the issue and is looking into a fix. Although there is no current information on how widespread the issue and so it's unclear whether any particular Google Home Mini unit is affected or not. It also only seems to have been noted for the smaller Home Mini and not an issue that has so far been associated with the original Google Home.
As for the issue, it is a very specific one and not one which just occurs when playing music. Instead, different users are pointing to different instigating aspects. For example, some users are suggesting that the issue only occurs when playing specific song titles. It is also suggested that this could be only occurring when the music (and maybe those specific song titles) are played through Google Play Music. Although the most common aspect is that the issue is triggered by playing music with the volume set to maximum. At which point, and following a 'few seconds' of playback, affected Google Home Mini units start rebooting.
One interesting speculation is that it could be caused by the bass associated with a track. In short, the more bass-heavy the track, the more likely the issue is to occur. It is not quite clear if this is actually a contributing factor or not although some of those noting the issue are suggesting that bass-focused tracks are more prone to the issue than tracks with less bass production. In either case, a number of owners have now reported a similar issue on both reddit and the Google Home Help Forum. The latter of which is where Google representatives have responded and confirmed that (a) the company is aware of the issue and (b) it is working on a fix. In spite of its awareness however, Google is still asking those who are experiencing the issue to let the company know by providing feedback through the Google Home app. More info on the issue, and how to provide feedback through the link below.