All underlying harddrives in our hypervisors run with a hardware RAID in either a RAID5, RAID6, or RAID10 configuration. This means that any harddrive can fail with absolutely 0 impact to your virtual server.
The failed harddrive can then be removed and a new one inserted and an automatic rebuild will occur without any downtime.
In the rare cases where a hypervisor does begin to experience hardware failure it is usually progressive, meaning the hypervisor may lock up and require intervention. In this case we would alert customers that have virtual servers on that hypervisor that their virtual machines would be migrated to a new hypervisor.
In this one case there would be a bit of downtime, usually about 15-25 minutes for most migrations.
However, this is the most rare and extreme case.