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.
Since the calibration routine isn't working properly, I suggest you take the laptop and new battery to the genius bar, mostly discharged 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.