I would first run SFC to make sure there is no corruption in Windows. I would also check for Malware with Malwarebytes.
I think there's something with his Chrome installation that is preventing Chrome from installing the new files when Chrome updates. Here's the way I would troubleshoot it. It will take a "wait and see" approach.
1. If he is syncing his Chrome data, turn off sync for that device.
2. Save his bookmarks. Completely uninstall Chrome using Revo Uninstaller Free. Make sure to delete all residual files and registry entries that Revo finds.
3. Restart and reinstall Chrome and his backed up bookmarks. Do not install any extensions at this time nor sync Chrome data.
If Chrome stays put through the next Chrome update, you know that either he had a problem extension OR the problem was in the syncing with his other devices.
If Chrome uninstalls again, turn off Chrome updates to see if it stays put.