Perhaps you have tried some of this...
How quickly are you plugging the HD back in after "ejecting" it and unplugging it? Perhaps if you delay a bit, or even a long time before re-plugging the HD it may work.
After re-plugging the HD back in, how long do you wait before deciding it is not being recognized? Perhaps after waiting more time, it will be recognized.
If you have more than one eSata ports on your computer, try alternating which port you plug the HD back into.
If you have access to another eSata HD (even temporarily) you could try plugging in a different HD after removing yours, to see if it is recognized.
Open Control Panel
and click Device Manager
. Then locate your eSata controller/adapter, and right-click on it, and select Scan for hardware changes
.
Try the Hardware and Devices troubleshooter. Perhaps it will re-establish connection to your drive: Control Panel-->Troubleshooting-->Hardware and Sound-->Hardware and Devices-->Next