Hey there, Milos.
It doesn't sound like anything that has to do with the PSU. If I were you, I'd backup any important data which might be on the HDD, just in case something unexpected happens. After that you should download the HDD manufacturer's diagnostic tool and run all the tests so that you see if there are any errors or bad sectors. If everything seems fine, go ahead and try the drive with a different SATA port and with different cables as well, to see if the problem still persists.
Hope that helps. Please let me know how it goes.
Boogieman_WD