I am having this exact issue with a mecer 2kw trolley inverter. Seems to drop by 2% every 2 days. Also just over a week old. I have been googling and stumbled onto this thread.
When i got it i charged it overnight to 100% without any load. Then i added a few items, very basic at around 230w load in total. It has been running constantly through loadshedding for the past week, but the behaviour is exactly the same as the Carlavdw has mentioned. has even gone down to 94% currently.
Very confusing indeed.
This is mine:
https://www.webdirect.co.za/mecer-2kw-256v-100ah-lithium-battery-820w-mppt-inverter-trolly