One of the symptoms of a failing disk drive is that reads or write take much much longer to complete. What's happening is the drive itself detects an error, and it retries, sometimes with many repeats, until it eventually succeeds. It's the repetitive retries that produce the slowness.
Note that because the drive itself is doing the repeated retries, and because it eventually succeeds, this won't show up as a disk error to the OS. As far as the OS can tell, the read or write worked, since no error was reported.
One other effect of this kind of disk failure is that sometimes there will be disk errors, and they will occur in the directory structure. These appear as apparently empty folders, missing files, and other loss of file-system structure. A "Verify Disk" may see these, or it may not. If a "Repair Disk" fixes these, they may spontaneously reappear again later, and sometimes not be fixable. Repeated attempts to Repair Disk will eventually prove fruitless, as the errors increase at a faster rate than repairs can fix them. Usually by that point, you're losing file data, so that becomes the primary symptom, rather than inexplicably empty directories.
When a disk drive is failing this way, it may or may not show up in the SMART status (see bottom of window in Disk Utility.app).
Yes, I've had disks fail this way: slow reads, slow writes, no SMART status warning.
The safest thing to do is get as much data off as possible, and onto another disk drive. Minimize the amount of writing to the failing disk, which means NOT doing things like replacing the OS, "Repair Disk", "Repair Permissions", etc. Anything that writes to the failing disk is more likely to be corrupted and become unfixable.
Think "abandon ship" instead of "plug the leaks".
TL;DR: Assume the disk drive is failing. Replace it ASAP instead of trying to salvage it.
