You didn't mention if you have a OBi 1xx or 2xx series device. The 1xx devices, by default, can't handle some other Chat client being configured to the same account. If you have a 1xx device, and you've also got another OBi or some Chat-based soft client running then that's your problem. If this is a 2xx device, then this isn't typical behavior, and I haven't ever experienced it. As long as Chat is on your GV account, and it's check-marked, it should just work.
I suspect you've got some unrelated networking issue going on with your home network setup, or with your obi configuration. If you want to troubleshoot this, I suggest starting from a factory-reset, plain vanilla OBi condition, with the very latest firmware update applied. Then, only add GV as your SP, and don't fiddle with any other settings. Leave it alone for long enough to satisfy you that it works consistently, before making any changes.