Redundant array of Independent Disks (RAID) storage technologies provide a way to secure information using one logical unit composed by distinct physical disk drives, allowing continued online status.
With RAID 1, data is written identically to two drives, and the array continues to operate as long as at least one drive is functioning.
Since RAID 1 operates as a mirror, replicating everything from HDD 1 to HHD 2, a RAID rebuild on one of this HDDs shouldn't cause the entire service to stop (controller dependent). If it does, is because the web host is intentionally stopping the entire storage or the RAID controller is unable to operate with only one drive.
Since drive capacities has grown at a much faster rate than transfer speed, the larger capacity drives may take hours, if not days, to rebuild. If the web host keeps the unit online, this operation gets increased. Putting the entire RAID unit offline to allow all the resources to be available to the rebuild process may be the best way to have everything back and running faster.
More detailed information at Wikipedia - RAID.