Because your 800 W coffee maker draws much more than 1000 W when it kicks on. It has a resistive heating element which starts out drawing much more than the rated 800 W. It's only after it's up to full temperature that it goes down to 800 W.
So there are lots of factors involved, some previously mentioned. Most inverters allow higher load for some brief time. Batteries have internal resistance which limits the power they can supply. Wiring has resistance which reduces the available power to the inverter. Inverters will shut down if the input power goes below some level.
Which of those factors is causing your issue requires more info, which may require measurements you don't have the equipment to provide.
The simple solution is to just use the propane stove to make coffee. Pour over cone filters make good coffee.
