A6 GPRS Power Supply

Hi everyone,
I have built a project that can alert you when there is a power failure by calling your phone via the A6 GPRS module. however, I've noticed the module can't work without a strong power supply and when the power is down the arduino (powered by a 9 volt battery) can't deliver enough current.
Until now I've used a smartphone power bank, but it's too clumsy for my small project and I'm looking for something more elegant.
Any idea someone?

Someone?

What is the downside to the power bank?

You need 2A peak, about 200mA average.

Choose your poison

Allan