The Chromecast integration has always had some reliability issues for some users. I am not sure if the root cause has ever been determined. But, for most users, simply running the Initialize() command on the device seems to get things working again. The Initialize() command is run automatically each time the hub is rebooted.
Thus, @danabw's advice to use a rule to run Initialize() every day makes a lot of sense, to try and keep the connection between the HE and the Google Home device alive.
