By exiting the client or 'hard cutting' your connection you will still be online for the whole duration of the 'PVP battle'.
If you pay close attention there are two 'Battle' icons, the crossed swords.
If the crossed swords are silver/gray that's the PVM battle and after losing connection monsters will stop attacking you and you should logout after around a whole minute.
If the crossed swords are red that's the PVP battle and you will only logout after it wears off.
That can range from 1 to 15 minutes.
PVP > PVM (meaning if you have the PVP battle and engage with creatures it will not change, they do not share the 'decay' timer)