I have a problem my notebook with ICH 9M and AHCI mode - doesn't work in hot plug mode for attached disk. I can dettached the SATA disk only through the notification area in Windows 7-64 - safely remove hardware. If I don't so, my disk will not appear again.
On systems where the eSATA port is managed by the Intel® SATA controller (using Intel® Rapid Storage Technology or Intel® Matrix Storage Manager), it expected that you need to stop the device before disconnecting the device.
Your system could be using a third party controller for the eSATA port, like a Marvell or Silicon Image controller, so you could check with your computer manufacturer for that to see if this would not apply for your system.