Kirk, you're the right track, re: a new controller. I find, though, it's often a motherboard issue. Two computers ago, I ran Win XP , then Vista on an Asus motherboard. No problems plugging/unplugging the drive. Then I rebuilt my computer with an MSI board, and it NEVER recognized the eSATA drives unless I rebooted, no mater what. I now have a new computer running Win 7 x64 with a Gigabyte board. Not only do I have two eSATA connectors (actually 4 including the 6GB/sec connectors) built in, but am using my older eSATA card. Usually, I have no problems with the built in connectors. Occasionally, the ones on the card require I go to device manager, click on hard drives, and have the computer look for new hardware. This always fixes the connection.
So, you might also try turning on your eSATA drives and going to the Device Manager to try to get the computer to connect as I mentioned above.
Nemo