One solution to this problem is to upgrade from a single drive to a RAID array. Simply put, the technology involves running two hard drives in tandem. One is used by the server, while the other keeps a constant backup of everything. In the event the main drive fails, the backup takes over.
After experiencing two hard drive failures on my dedicated server, I paid my provider around £100 to have a second hard drive installed for RAID. While a bit pricey up front, the cost of downtime for me was much greater. I not only lost revenue when my sites were down, but also had to spend a significant chunk of time reconfiguring my server and uploading my data. A RAID array was a no-brainer.