As you have phrased the question the rabbit is dead every time. Rabbits aren’t hares, they can’t run for any distance. So in an open field pretty much any dog will kill a rabbit. I saw a fat old corgi chasing a rabbit around an open paddock for about 10 minutes once. Eventually the rabbit grew tired and the corgi killed it. A fit young dog will probably run a rabbit into the ground within 5 minutes.
In a more normal scenario it depends entirely on how good your dog is and where the closest shelter is. The only way a rabbit will survive a determined dog (ie any terrier) is if it can make it to shelter before it’s caught. An experienced dog will know enough to turn a rabbit away from shelter such as hollow logs or netting fences. Unless there is a lot of different cover available an experienced dog will kill any rabbit it can find in the open three quarter sof the time. Less experienced dogs, or dogs too slow to turn a rabbit, will always lose their prey if there is any cover at all within 20 metres or so.