This has come up out of nowhere, but for some reason whenever my battery reaches say 70%, or 64%, or something random like that, my MacBook Pro will instantly turn off. No sleeping, no warning, just instant off. It will then not turn on unless I plug it into a power source.

Now it will work perfectly fine all day off a power source, but I can't use it more than half an hour without it shutting off on me. It's not even dead.

Any ideas?

What's the cycle count for the battery? (From System Profiler)

Has it been recalibrated recently/at all?
I'd say try calibrating it and reset PRAM and SMC/PMU (or however they call it for your model) at the appropriate time for the recalibration....

Sounds like the battery took a dump, these things sometimes happen. You best bet would be either (if your Mac is still under warranty) and call AppleCare or get a new battery from somewhere.

Charge Information:
Charge remaining (mAh): 4719
Fully charged: Yes
Charging: No
Full charge capacity (mAh): 4880
Health Information:
Cycle count: 244
Battery health: Good
Battery Installed: Yes
Amperage (mA): -1645
Voltage (mV): 11722

Try recalibrating it. With that cycle count it should still work better than you describe.