GoDaddy LiveChat support is from Monday to Friday
but currently not 24/7, only from 5AM to 6PM (UTC-7)
And you are right, sometimes even on Monday from 5AM to 6PM (UTC-7)
the LiveChat button is disabled, this is may be due to some internal issues or the team is not present because if the team is present then it should be enabled. Anyways whatever going on behind the scene we can't figure out but its bad user experience and they should solve this thing. Even this issue is discussed here you take a look at the following link:
Why is Live Chat not 24/7?