For me, this started when I updated to 10.3.1. I have a 5s. Clearly this is a problem that is happening on multiple devices. In addition to battery suddenly draining rapidly, my phone won't charge when it starts behaving this way. It's always fun to be traveling when your phone stops working.
I tried a restore of backup initially, but it kept hanging on iCloud settings (also a known issue). I gave up and restored to factory settings when I was able to get a little bit of a charge. Like others, I had no apps running and put my phone in airplane mode.
Restoring to factory settings fixed the issue for a week - until I hit another hotel wifi network. I thought maybe that was the problem, so I rebooted the phone and kept it on cell networks. Both times the problem occurred, I was on hotel wifi.
When 10.3.2 came out, I hoped I would never see the problem again. Alas, it's back today. On my home wifi. The phone just lost all charge while connected to laptop/iTunes and restoring to factory settings. Sorry I don't have any solutions to add. Just more problems.