Is the floppy ear inflamed at all? Thick? Often when they get ear infections, or even aural haematomas (I'll explain in a sec) they let their ears flop as its painful. It could be that? Its hard to know without having a look at the ear and inside it.

Aural haematomas happen when they shake their heads due to fleas or ear irritations like flies... and they burst a blood vessel in their ears and it fills up slowly with blood. Often if they are bad, vets will put a drain in to let the blood drain out slowly, or they just pull it out with a syringe and see if it fills up again before going through anaesthesia. Most of the time pulling the blood out with a syringe & needle doesn't work, but its good to know there are options.