I'm in the same boat, with an iPhone. To be clear (because I've seen other threads about a different problem), my zip battery seems to go dead in about 2 weeks instead of the advertised 4-6 months. I've had different zips for a few years now, and the last time I had this issue it was solved by going into the fitbit app on the phone and turning off an option that read "all-day sync". However, that option is no longer present in the app.
I've recently turned off Background App Refresh in the main phone settings for the fitbit app, but based on other forum postings I'm not optimistic that this will have any affect. What I believe is going on is that the zip and the phone are trying to sync all day long and that use of bluetooth radio is draining the little battery in the zip. But that's a guess, because that seemed to be the problem in the past.
