After 3-4 days of non-use, I found my 2005 3-hatch with the battery apparently completely dead (after no previous issues). No lights, power locks, etc. I assumed I just left a map-light on or something, and called AAA for a jump.

They come, jump the car, it starts. After a few seconds, the AAA guy turns it off, and tries to turn it on again under it's own power. Doesn't even try to crank. After that, the car couldn't be started again, even with the jumper cables hooked back up - it doesn't even try to crank at all. There is, however, a blinking red key-shaped light on the dash (the immobilizer, I'm guessing?)

AAA guy gave up, and left. 10 minutes later I go back to the car to double-check, and find it 100% dead again (no power locks, no dash lights, etc).

What could be going on? Can batteries die so suddenly? And why won't the car start even when hooked up with jumper cables?

What's my next step

[Side question: is there a way to manually lock the rear hatchback door?]

Thanks for your help!