Hello Slugger,
Sorry to hear your still having problems! Was the machine fixed under the manufacturer's warranty or a service plan, such as Geek Squad's Black Tie service plan (I think thats the correct name)? Either way on such a new system, unless you've been giving it a good kick to the side when you get frustrated with it

, I would take it back to get it fixed again - as painful as it might be to be without your system!
In the case of the latter (paid service plan) Geek Squad and some other companies offer a third time replacement or "no lemons" guarantee, where they'll give a new one or "comparable" replacement. If it were the MOBO, the new HDD, the PSU or even something completely unrelated causing a conflict, it should have not been returned to you without being fixed!
Now, if it was the mfgr's warranty
and it's a software issue - I doubt anything short of a problem they caused when they fixed it would be covered.
Honestly, that's the easiest way to fix it, especially in light of the fact that you DID pay for the warranty - either separately or as a portion of the total cost of your computer - so get your money's worth out of it! (Sometimes you have to demand satisfaction to get them to do their job correctly and thoroughly.)
As far as looking into it yourself, Check the Event Viewer: [Click

rb:; Type
eventvwr.msc; Press
Enter.] Look through the events
leading up to,
as well as after a KNOWN time that a "restart" rendered the drive unaccessible and note any critical/error or other relevant event's. I would then repeat this with the "shut down & unplug" method you mentioned, where the drive becomes a valid, working drive, and then compare the two sets of events for any anomalies.
Also keep an eye on Device Management: [Click

rb:; Type
devmgmt.msc; Press
Enter.] Watch both the Drive itself and the drive's controllers. The drive may show up as "Other Devices" when it is not working correctly, under certain circumstances.
As long as it will not void your warranty to open the case (they'll usually use "Void" tape to determine this, so look for any type of tape first, and proceed at your own [warranty's] risk!), you could remove the drive and test it offline again with SeaTools (using USB connection) - or did you do that already, I was unclear from your post, esp. about the results.
I would probably tend to lean toward either the hard drive being a defective one (attributed to poor quality control or components - and hopefully not some root cause in your system!) or my original suspected cause, the Power supply. It would be nice if you had another,
somewhat similar system to swap PSU's with to help rule that in or out!
Good luck,
Mike 