BLE Peripheral

I have an Arduino (ATMega32u4) Adafruit board (5V). I will need BLE capability as part of this device. The Arduino will always be in a deep sleep state until it gets an external interrupt (via a water flow sensor).

Once the interrupt occurs, it will measure the water flow until it stops, then submit the flow via BLE. I purchased one of these Adafruit Bluefruit LE SPI Friend - Bluetooth Low Energy (BLE) : ID 2633 : $17.50 : Adafruit Industries, Unique & fun DIY electronics and kits. So, ideally, the BLE module is sleeping as well until it needs to submit the data.

It's a perfect module, except I can't put it to sleep. I've posted on their forums about it, and it's just not designed for it. https://forums.adafruit.com/viewtopic.php?f=53&t=138831&p=690669#p690669

Does anyone have a suggestion for a BLE module (or 5V board) that can power off the BLE module until it's needed? I'm ok with a brute force power down as well (transistor/FET), but even with the 5V pin on the BLE module pulled down it stays powered on (see forum post).

Thanks.