I have a 2013 Fusion Titanium (as well as a 2017 Sport) and replaced the original battery after 5 years, which I thought was a good battery life cycle. The new battery went bad after 2 years, which surprised me, as I had installed a new Motorcraft battery myself, not wanting to pay the $150/hour shop labour rate for something I could easily do. After the 2 years I started getting the message "system off to save battery" and then accessory power would not run when the car was turned off, similar to other reports on this thread. I took the car to the Ford dealer where they ran tests and pronounced the battery bad. Since it had been bought from Ford but installed myself they replaced the battery under warranty, but charged me for the diagnosis.
As it turns out I was not aware of the battery monitoring system the computer in newer cars now have, not just Ford. This system reads the length of time the battery has been in service, and needs to be reset when replacing the battery. When not reset the computer thinks the battery is old and tells the alternator to charge at a higher rate than a new battery needs. This can ruin the battery - probably what happened to me. This is not well known and when I took my car to the dealer because of the bad battery, they replaced it but forgot to reset the BMS. This is how I learned of the issue, and think that many others on this forum may have the same problem by not doing the reset because they are unaware of this issue. I went to the manual but it does not explain this (page 251). It says: "When a low voltage battery replacement is necessary, see an authorized dealer to replace the low voltage battery with a Ford recommended replacement low voltage battery that matches the electrical requirements of the vehicle. To ensure proper operation of the battery management system (BMS), do not allow a technician to connect any electrical device ground connection directly to the low voltage battery negative post. A connection at the low voltage battery negative post can cause inaccurate measurements of the battery condition and potential incorrect system operation." The car went back to the shop and the dealer apologized for forgetting the reset (I was still getting the "system off" message), but once reset it has been fine ever since, and runs on retained accessory power for 10 minutes before shutting off. The dealer has a proprietary computer system to reset the monitor, so again will charge for this at shop rates if you install your own battery. There is a secret fix for DIY BMS reset. Thanks to someone who posted the fix on YouTube - here it is. I think this might solve the problem for a number of forum members who like me still like to do some of my own maintenance.
For the 2013+ Fusion, turn car on, but Do Not Start. Flash high beams five times, and hit brake 3 times releasing fully each time. Within 5 seconds battery light will flash 4 x showing a successful reset.
https://www.youtube.com/watch?v=I4sG3ufFiXs