this will happen if the user’s home is not accessible at the time of the refresh.
This is documented as not supported in the Limitations in snapd topic, precisely because of this behaviour.
Edit to add: in particular, it’s highly unlikely the data has been deleted, but it’s probably inaccessible to the current revision of the application. As a workaround, with the user’s home accessible, try snap revert chromium, followed by a snap refresh chromium. This will only work if the revision of the application that has the data is still installed (see snap list --all chromium for example, as well as du -sh ~/snap/chromium/[0-9]*)