Yes you can leave the cooking oil in your deep fryer without needing to empty the oil every time you use it.
What I do is allow the cooking oil in the deep fryer to cool down and then put the lid that came with the deep fryer on the deep fryer to keep any bugs or anything out of the cooking oil.
You could also place some tin foil over the deep fryer to keep the oil from getting bugs or anything else in it.
I change my cooking oil every 6 months or so when the cooking oil starts getting darker in color.
Sometimes you might need to change the deep fryer cooking oil sooner depending on how often you use the deep fryer to cook the foods in.
I don't deep fry foods often so 6 months between cooking oil changes is enough for me.