The notebook is supposed to enter into safesleep mode once it goes to sleep with less than 10% battery remaining. It records everything to hard drive and fully powers down so it doesn't use more battery power keeping the memory alive.
However in your case it doesn't have enough energy left to spin the hard drive up and record everything. In fact, if you've only been browsing, or reading, the hard drive might not have even been on while you've been using it - and suddenly it spins up, spikes the power consumption while writing the memory to the drive, and then shuts down due to low voltage.
You can try the calibration routine with one modification: when you get the 10% warning, put it to sleep and let it sleep for 5 or more hours. Then plug it in before you wake it up.
If the calibration routine still isn't working properly, I suggest you take the laptop and new battery to the genius bar, discharged to 10% so they can run it down there, and let them handle it. They'll either get it to calibrate, or they'll replace the battery if it's a new Apple battery.
This shouldn't be happening, so don't hesitate to have them support you.
If you're out of warranty, or you're using a third-party battery, then you might try applications such as http://www.axoniclabs.com/DeepSleep/ which force the laptop to go into safesleep mode (hibernate) rather than sleep mode.
If you are using a third party replacement battery, talk to their technical support. It's obviously not fully compatible with your laptop if it's not calibrating correctly. It could be that it will never calibrate if they've skimped on the smarts inside the battery.
If nothing else works and you can't afford to repair the laptop or battery once the genius bar tells you what's wrong, don't keep using it once it gives you the 10% warning. Put it to sleep until you can charge it, and repair the laptop or replace the battery when you can get to it.