MFLASH 5000mAh Rubberized Power Bank – has been added to a raspberry pi as an uninterruptible power supply (UPS). It was on a Black Friday sale for $10, down from $25 and is connected to the Pi that died during our last power events (off, on, off, off, on). It had to be reinstalled from scratch and it would have been fine if the power had not cycled like it did.
It looks like it can simultaneous be charged from the pi power supply and power the pi through its 2.1 amps out port. Both connections are microUSB.

Two weeks later the battery is showing a full charge and the Pi has run continuously without issue.