The same has been happening to me recently with my SE on 10.0.2. I've done a hard reset and it still happened so I drained the battery fully. My SE still has warranty and isn't old, so I'm hoping it's not a bad battery. It'll drop, say 1%, and then drop another 2% within another 1 min of use (browsing the web or something). It also dropped like 10% when I slept (roughly 5-6 hours of doing nothing) and it use to never do that. It just started randomly happening, both prior to my hard install and after, and I'm not sure what started causing it.
Another issue I'm having is, even though my email is set to push on iCloud, emails don't show up unless I open the mail app and let it "Check for mail". I'm not sure if it makes a difference, but I also have Outlook and Gmail accounts, but I de-selected mail on them and only have contacts and calendars for those accounts (and they're also set to fetch hourly and iCloud is set to Push).