they like to turn themselves off, it's one of their favorite things to do. My favorite trick is when you try to start them up and everything looks normal until they just turn off again.

It might just be a sign of a weak battery. Lithium batteries don't have very good capacity at cold temperatures. Put it on a charger for a while and then press all the buttons at once. Or whatever the reset sequence is for your particular model. On my edge 800, you push the two buttons on the front and then the power button.

What temperature did it get down to on your ride? I generally keep mine on an external battery, but I have had no problems on long rides in the mid-20F temperature range. Going to test this whole theory on a ride on Saturday, temps at the start look to be in the mid-teens.