Have you tried switching SATA connections on the motherboard? If you've got 4 SATA connectors, they're probably numbered 0, 1, 2 and 3. You may have used Zero as the first one, but your BIOS will probably merrily accept any of those as your Boot Device.
Assuming you've done this, but are still getting drive errors after a few minutes, then you might check your Windows Control Panel and see what kind of POWER SETTINGS you've got.
If this is a Desktop Computer, I'd leave HARD DRIVE POWER to an "Always On" choice. If the hard-drive is a modern "green" drive, it will have some power-minimizing smarts of its own, and should keep funneling "I'm still avaiable!" messages to Windows, even in a lowered-power condition of its own.
I much more trust devices to power themselves up and down rather than pretending Windows Programmers know every device in the history of computers.
So I leave Windows Power Settings to ALWAYS ON and let devices generate their own messages. Otherwise, I think I'm always asking for cross-pointed fingers - "It's the OTHER's fault! I'm fine - IT'S bad!!"
If you've got a 2nd PC, you might detach this suspicious hard-drive and connect it as a secondary drive to that other PC.
Sometimes, I've used those little USB-to-IDE/SATA connector kits to do this, so I don't even have to open up the second PC. Or I could use a notebook, too, for that matter.
I'd be looking to 'prove' the hard drive's working condition - "Does it generate flakely errors on another device?"
If the flakey behavior goes wherever this hard-drive goes, then you have your answer - "time for a replacement drive."
If the behavior is with that one Windows Machine, then it's probably a Setting - such as POWER.
Or perhaps it could be a power-supply ready to die. (That's a very VERY remote possibility, but if the Drive works fine when attached to another computer, and my Windows Settings seemed to be fine, then I'd probably replace the power-supply as my Next Guess. It's relatively easy to do... RELATIVELY. cough cough.)
If you write back with a precise description of a brand-name computer and its model, then I'll understand "replacing power supply" will not be an easy option because some are quite proprietary and thus far more expensive than 'standard' power supplies.