I once measured microcontroller current consumption very thoroughly. I've studied Atmel and Microchip controllers, but would think that my observations below apply to most other brands:
1) A microcontroller's current consumption IS NOT constant. It varies all the time, sometimes an order of magnitude or more. You need to take several reading over -let's say- 1 minute period and then average them.
2) You'll find that the current consumption varies as the controller enables the ADC ports, turns on and off the different outputs, or reads/writes on any external bus (I2C, SPI, RS232).
3) It goes without saying that different clock speeds DRAMATICALLY change consumption.
4) There are other features, like brown out detection or timers that have an impact also.
5) When one is squeezing the last microamp, even trivial things live leaving input pins floating increase current. If you have unused inputs, either use a pulldown resistor or, if the architecture allows it, make the port an output and set it low.
6) Most datasheets discuss strategies to reduce current. Study those.
EDIT: After re-reading your post above, I realized that you are using a pre-built module and some of my advice is not applicable in this case. I'm leaving the message however, since the recommendations may be useful to other readers.