Battery drains too fast when device is Shut Down
Firstly, try disabling WiFi before you sleep or power it off in case that is preventing sleep or waking it excessively.   

I would get Apple service to run a battery diagnostic. This is the sort of thing they can very rapidly diagnose and easily measure if they have it in for service. 

You should have months of stability if you charge your battery to 50% and then power it down. That’s what Apple recommends for long term storage. Something isn’t proper and warranty / AppleCare likely covers repair the bulk of them. Even if you’re out of coverage, get a quote and free diagnostic. 


https://www.apple.com/batteries/maximizing-performance/


Support is easy to get started over chat or phone - https://support.apple.com. You are doing everything right and I hope it’s not a flat battery that you end up having to pay to swap when it becomes too unfit for your needs.