I had been using RST 11.7 with ASRock X79 Extreme 6 (i7 3930k) and Windows 7 x64, and I also met with the same problem. Reinstalling RST 11.7 or 11.6 and ASMedia SATA Host Controller, updating the so-called BIOS ended in vain. But If ASMedia SATA Mode in UEFI Setup Utility is "Disabled", RST user interface can be open.
Unavoidably I am using "Standard AHCI 1.0 Serial ATA Controller" in place of RST, because I need 8 SATA ports.