I've read in some forum that the battery life is rather short for Iriver Story e-book reader, vis-a-vis other similar readers in the market. It's been claimed that without playing music at all, the battery would last about 5 days at most, and would read just a couple hundred pages.

I wonder how true this is. I intended to purchase one, but this gave me pause. Could owners of Story in this forum please advise?
Well, I've just finished my first book in it, so not conclusive.
It's 3 weeks since the iriver was connected to my computer for file transfer, charging it as well.
Since then, I'm using it occasionally and turning it completely off when not reading. I have read the above mentioned epub (over 1000 page turns), some 200 page turns of pdf comics as a break, and played around with some mp3's and no recharge needed yet.
I'm in the lower third of the battery though.

If you focus on reading and don't play around with accessing menus, notes, comics, music etc. I think that you could take for 2-week holiday reading without recharge.
Is switching off necessary? I understand it, E-INK uses no power at all when it is at its rest state, when words have been displayed.
The eInk screen doesn't, but so what? It's a computer and, like all computers, the CPU, RAM, etc, all use power, even if the screen doesn't. Does your PC stop using power if you switch the monitor off?
Well my understanding was that they use no power when not changing the display - has anyone ever tested this?
The battery works just fine=)
I read a lot.
5 books in a row, 200-500 pages each, with a lot of pauses, stops, going backs, turning on and off in that time.
But if I combine book and music it takes a day and then recharging
They do use power, even if minimal.
They have a RAM which must be kept "turned on", for example, otherwise at each page turn the device would have to
1) load the kernel
2) load the reading application
3) load the file
4) load the last read page
5) change page
6) turn off

Which is impractical.
The screen is, of course, the element of a PC or PC-like device that consumes the most (think of mobiles, netbooks and smartphones, the screen is the single element consuming the largest quantity of electricity) so the fact that the e-Ink screen consumes energy only when changing page improves significantly the duration of the battery.

I have made a couple of simple tests, and I noticed that if I turn off the device each time I stop reading, the battery of my device (a HanLin V3) lasts for about 10 days (reading 80 pages per day on average), while if I never turn it off it lasts only 6 days.

Of course, turning on and off your reader increases the energy consumption, so if you make a lot of breaks while you read you're better not turn it off every time you stop, or you end up sucking even more energy from your battery instead of saving it. Turning it off helps if you make long reading sessions with no breaks.
The screen uses no power. As I said, the other components of the machine will use a small, but significant, amount of power while the machine is on. That's why the recommendation with all such devices is to do a full "shutdown" if you're not going to be using it for a day or two.
And my Mini has been on standby or active (aka reading mode) since november without having had one recharge since. I've lost one bar out of four now...
Yes, different devices differ greatly in their "sleep" power characteristics. The Sony PRS-600 drains its battery in about a week if you don't use it. The BeBook Mini does seem to have one of the better power-management systems, but at the expense (so I've read), of sometimes missing button presses due to not "waking up" quickly enough.