I'd also suspect it's the batteries based on your earlier answer, though I'm a bit surprised, if they're actual Leica ones, that they're on their way out after only a couple years of use (though unknown is when they were made).
I have five batteries, one of which is probably from late 2009 (bought the M9 used in 2010) and two from late 2010. All still seem to work pretty normally, though this winter, for the first time, I had sudden shutdown problems with my M9 in cold conditions around the freezing point and lower. It may have been a combination of older batteries and not having updated to the latest firmware version with improved power management (haven't updated for a couple specific reasons).
I'm not familiar with the MM firmware versions and how those might mirror the M9 firmware updates, but your problem also doesn't seem to be specific to the camera, for the most part.
In any case,
here's a handy firmware reference site. Of note, with Leica's update 1.196 for the M9, they stated the following:
It is the nature of Li-ion batteries that the capacity weakens after a certain time. We recommend replacing the batteries for the M8 and the M9 after 3 years at the latest. Heavy usage can even accelerate the aging process, and then batteries should be replaced earlier.In case that the total amount of pictures, that can be taken with a certain battery, is significantly lowerthan before with Firmware 1.196, we recommend replacing this battery.