My understanding is that modern harddisks will remap bad sectors automatically during normal operation:
A modern hard drive comes with many spare sectors. When a sector is found to be bad by the firmware of a disk controller, the disk controller remaps the logical sector to a different physical sector. In the normal operation of a hard drive, the detection and remapping of bad sectors should take place in a manner transparent to the rest of the system.
However, automatic remapping of bad sectors only occurs during write operations. To remap all the bad sectors on the hard disk, you will need to low-level format the HDD using the manufacturer's provided utility.
If bad sectors continue to develop even after low-level formatting, it won't be safe to use anymore IMHO. Better to get a new one than to risk losing your data.