You need to break down the brown stain. The brown stain is probably oxidised iron compounds. But no need to tackle it like that. I think this is one of those questions that borders between Chemistry and Biology:
Banana stains seem to disappear over time, right? That much food is too much to waste for bacteria and other organisms living on the floor. How do they break it down? Enzymes of course! So I would suggest using an enzyme-based washing powder.