For my sins at one time I did some development on Playbooks, and one of its quirks was indeed that it apparently does die when the battery is very low. I say "apparently" because all that's needed are a nice dose of patience and a proper 1.5A USB DCP charger such as that supplied (the one supplied says it's 1.8A). A bog standard USB port or charger wouldn't ever work for me as far as I could ever tell once it'd got itself into a very low energy state.
You have to leave it for quite some time under charge, but eventually it will recover. I can't remember how long it was on charge the first time this happened to me, but I'd forgotten about it and had given it up as broken. Anyway, miraculously when I came by it again some time (possibly a day or two) later after being on charge, it booted up.
Now today I can't remember the last time I powered up my Playbook, it's many months, but I took the opportunity just now to power it up and charge it up, but coincidentally and ironically, sadly the magic smoke has just escaped out of the original Playbook charger, one of those sealed units with little chance of redemption without engaging a Dremmel, so it's now headed for landfill.
Despite those many months of doing nothing in a drawer (after that first time, I always fully switched it off rather than leaving it in standby) it started up without any need for charging after all, but I am now topping it up on a different DCP port at just shy of 1.5A anyway!