You didn't say what OS you use; I presume it is XP or Vista or something similar.
1) If you open up your "Computer" explorer window where you can see the various drives listed you can right-button mouse click on the drive and it'll bring up a menu that sometimes has an "eject" option. This may help, though isn't the primary means to solve your problem.
2) If you look in the task bar over on the right side there are icons, one of which has a little green arrow / streak.. it may be hidden unless you use the expand arrow on the taskbar icon area to show the hidden / inactive ones. Anyway right-mouse-button click on that, it should be the "Safely remove hardware" icon. It'll let you pick a drive or device and then give you a menu option to safely remove it. This is the PRIMARY way you tell MS Windows XP / Vista that you want it to completely stop using a given drive, flush data to it, and not permit further access to it pending its removal. Sometimes it won't let you complete the operation to logically disconnect it because programs may still have that drive "open" in explorer views or have open files on the device that they haven't even closed yet. In that case you'll have to close those programs or files and try again to get it to flush the data and permit the device removal. Unfortunately this is a typical example of Microsoft's half-implemented brain damaged design -- it can be DIFFICULT or to the casual user who doesn't know how to jump through hoops IMPOSSIBLE to actually get a view / access to the drive AGAIN IN THE FUTURE *UNLESS* you actually physically disconnect it or power-cycle it which sort of defeats the purpose of a software controlled "online / offline" switch. They SHOULD have had the same little utility let you see all physically available devices and just CHOOSE which ones will be ONLINE / OFFLINE and change back and forth between those at will. Sorry.
3) If you go into the "control panel", "system / hardware", "device manager" type screen you can look at a list of the system devices and find that particular drive. If you select it and bring up one of the several properties tabs you may be lucky enough to eventually find menu options controlling something along the lines of : "Permit cached / delayed writes -- optimize for speed" versus "Deny cached writes, write data to device immediately, optimize for quick / safe removal". Pick the "optimize for quick removal" / "disable write cache" settings and that'll mean that unless programs have actually got open files and outstanding buffered writes (within the programs themselves) the OS will quickly synchronize the data to the device and stop accessing it, thus making it "safer" in the case it is removed or loses power. Unfortunately this is STILL not good enough unless you complete the "safely remove hardware" process / menu which is in a TOTALLY different place in the UI, so this stuff isn't exactly convenient to manage / find / use by being all together in one easy to find menu . And of course once you do tell it to remove the device you can't easily reenable it unless you power cycle / physically disconnect & reconnect it which is what you're trying to avoid in the first place.
4) Also in the "device manager" you can right click on a device and actually select to "DISABLE" the device in the current hardware profile, and amazingly you can also "ENABLE" a disabled device in the same place. Unfortunately this is neither conveniently located nor intended to solve your particular problems, so it really isn't a good (or even necessarily fully safe/effective) solution.
Basically eSATA sucks worse than USB / firewire from the standpoint of OS / driver level hot plug support, and even USB / firewire are not well supported for "soft removal / reconnection" in MS Windows as compared to a true physical disconnection / power-cycling process.
On Mac / UNIX you can just click on the drive icon and tell it to stop / start using it, but I guess that was too complicated for Microsoft to be able to properly implement after N generations of OS since Win 3.1.
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