Do you have the latest AHCI driver? Do you have AHCI enabled? AHCI provides hot swap support and power management to removable SATA devices. Install driver, then enable in BIOS. Not vice versa.
If you can't find an AHCI driver for the card, then you can enable Win 7's own AHCI support but I believe it's an old driver. But since the card has an eSATA connector, I assume it came with a driver CD.