The blinking red light does suggest the battery actually had run down. If you had been using the PE for 4 hours or more, this would be expected even if the battery status showed higher. Your LCD turning off and being unresponsive indicates the power had quit, too. Note that in a sudden power failure like this, the eInk side will continue to show whatever it last displayed (an eBook, a Journal, or whatever).

If your battery is running out in 2 hours or less, you may want to contact Tech Support since the battery itself may be flawed (although I've heard essentially no reports of battery problems on the PE, while the EE had more than a handful of reports on these forums of needing the battery replaced).

As for the low power popup, I get this on my PE from time to time when the battery status is showing at leat 50%, just like you. A quirk, I guess, but perhaps my battery is doomed, too?