Yes, services can become unavailable for many different reasons, eg, the server the service is running on could go down, someone might delete the service and so on. There is no guarantee a service will be available.
In the case of the ArcGIS Online basemaps, we have a lot of servers and back up servers to ensure that the services are running. However, in your case, you are accessing a service running on someone's instance of ArcGIS Server. Luckly, this is a server run as part of a lab at Esri, so I've asked the owner to fix the problem. Hopefully it will be resolved in a day or so.
Thanks,
Mike