If you believe that the software that has tested it is reliable then you must replace it ASAP. Many HDD manufactorers have their own diagnostic tests for their drives. Test the drive with this software for a second opinion. The most important thing is to get any data you want off the drive so you can test and maybe replace without the threat of data loss.
- there may have been a suspect area of the media which couldn't be read, and the disk may have already reallocated those sectors somewhere else. In that case, the raw rate should be stable and not changing.
- there may be an issue with the heads which is causing ongoing read errors. In that case the raw rate will keep increasing.
The latter would be a lot more cause for concern. In either case I'd do as Wamphryi suggests and make sure you have another copy of the data just to be safe.