Sounds like your problem might be fieldcraft rather thanh shooting. Try going out without your gun with teh sole purpose of getting as close as you can to the quarry. Remember noise, movement and smell can all give you away. If you don't have a gun you wont be distracted by wanting to actually shoot. If you havnt had a lot of shooting practice you will need to be a max of 25 yards away from the rabbit to ensure a clean kill. With practice this is quite possible.
If you are out at night remember to cover your face and hands - they stand out very white to the rabbit in teh dark
HTH