We decided to switch to the Arduino Zero for our microcontroller. Due to Beaglebones high power consumption of 2.5 Watts, it would be unrealistic to try and power this device for weeks.
We are still going to store the data on a SD card and have the Arduino Zero's built in RTC (real time clock) be used to timestamp each signal stored. The Arduino Zero will be in sleep mode and an analog device that can pick up signals will wake it from sleep mode and begin recording. This is to save power and have the device's battery last as long as possible.