If both are reporting the same thing it might actually be going down briefly. Since it seems to happen at regular intervals you should try to ping your site around when you get the notices and see if you lose the ability to connect from your location, too. You can start a perpetual ping from a command prompt in Windows by using:
ping -t www.google.com
If you lose connection to the server as well it should be safe to assume the host itself is actually having issues every 30 minutes and you should contact them to resolve it. That could be when they run their backups, which would increase the load on the server and possibly cause timeouts.