I am really sorry for this issue you are experiencing.
I see your motherboard has two SATA controllers, is the Intel® SSD connected to the Intel® Z87 Chipset? If not, please do so. Making this change will most likely require the operating system to be reinstalled.
You may want to use latest firmware for the Intel® SSD and latest motherboard BIOS.
I have moved the drive to the Intel Chipset, and installed the latest version of the BIOS as well as the SSD firmware (as of the Intel SSD Toolbox v3.2.1). I also reinstalled the OS.
The issue still persists, where the drive will randomly "disappear" and cause a BSOD. Is there a solution to this issue?
There is only one other SATA device connected. Its is a DVD-RW drive connected to the same Intel controller as the SSD.
The system behavior is the same, regardless of if this device is connected or not.
The ASMedia* drivers were updated along with ther others.
I am unable to complete a Full Diagnostic Scan from the toolbox. The drive "disconnects" before it is able to complete.
Sometimes you can get better results with the Microsoft* version of the SATA controller driver instead of Intel® Rapid Storage or ASMedia*. If possible, you may test the drive in a different system and see if the issue follows the SSD.
You may also consider replacing the drive by contacting your nearest Intel® support team.