I thought I'd see what happens when the Shimano Di2 battery completely runs out. The instruction manual says that the FD fails first, followed by the RD. This is roughly what happened but it took a while.
I first noticed that the green light turned to a red light indicating around 25% charge about 200 miles ago. I kept riding and yesterday, finally the FD failed, and I got the 5 red light flashes saying 'no charge'. I was on the small chainring so was able to get home just shifting the RD. I went out today and it obviously recouped some charge as I was able to shift the FD to the large chainring and back again before it failed again. I continued, shifting the RD just one sprocket as a time rather than using the multishift and about 13 miles later the RD also failed with the 5 red light flashes coming on.
I was able to easily make it to my destination in the gear I was left in and have now put the battery on charge.
I now know roughly how long I've got left when it starts showing the red light in future and thought this may be of interest to someone out there!