RememberThe5th :
Check for Sata if pins are aligned. Other may be moisture, dust etc. I really don't have idea.
It could be that motherboard from HDD is dying or other stuff.
If your HDD is Seagate Download Seatools and it will check for bad sectors and etc.
Its better be safe than sorry. Well i have mine for 24K hours.
Does sata connector feel like loose, or is it stiff?
As for sata cables, I tested three, an old one I had, was pretty dusty, so I traded it for a black one that came with the motherboard (was in it's box for a few months), when I noticed the problem, I traded it for another black one, smaller. The power connector feels so so as for being fixed. It really seems like it comes from the power connector in the HDD itself, since everything else is working fine. There is a thing that gives away that the problem will happen, though... the computer takes many more seconds to show boot screen, as if it was trying to find something, but couldn't. In this new build the HDD is in a vertical position, which also made me question if the power connection could be being affected.
The case I'm using now is a Thermaltake C21 versa, which has ports for the 3,5 HDD in the back in a vertical position, since the SSD in mounted in the front of the frame, the cabling is a little awkward, but everything seems to be well connected.
(EDIT)
I also would like to thank you for the support and telling me about the seatools, Just used it, all tests approved, but now I know where to look first in any other case like this.