I have had this happen multiple times over the life of my C-Max (2013 Energi, now with 76,000 miles). Fortunately, it has only ever happened at home, so I've always been able to jump the car. And then everything is fine again. Sort of.
The first times it happened, my Ford shop told me I needed a new 12v battery -- and they replaced it. Fair enough. Not long before the problem happened again. I thought perhaps it was because we'd left seat heaters on, or a fan on, or radio, or something. We did get a small clue, that the radio wasn't working. My Ford shop couldn't find anything, anywhere in the Ford system. The next time it happened, I pushed harder, and the dealer searched the Ford tech service bulletin (TSB) network in search of responses/solutions from other techs anywhere worldwide who might have encountered and dealt with the problem.
Long story short: they found one TSB notice and used it to completely reboot all of the car's software (don't ask me exactly what systems) -- a process that took about 3 hours. And that has worked great for a couple of years. This last time, a couple of months ago, my wife told me the radio had stopped working. Fearing that this was a warning of what was to happen, we left the car out of the garage to make it easier to jump. Sure enough: in the morning the 12v battery was dead. Another jump, and it was OK, but after driving around a bit to get things charged again, the radio still wouldn't come on -- until suddenly half of the central SYNC screen lit up, the radio half-started, the rest of the screen filled in, and the radio was back -- as if it required a set voltage from the battery before it would work work properly.
Have just taken it back to the Ford dealer. This time, they told me they replaced the APIC -- the radio module. They did this for free, so I'm not complaining; the car is way past warranty. But I'm not convinced the problem won't happen again...
S-o-o-o: two takewaways there: 1) consider the whole system reboot (which may be under warranty for you); and 2) consider the APIC radio module if you're getting the same warning sign of the radio going dead before the whole battery goes dead.
Hope this helps some folks.