The longest period of time I have read about where a U Boat was depth charged was in WWII. A particular boat(Can't remember which one) was depth charged for something like 9 hours off the coast of Hiafa in the Med. The crew vcouinted something like 240 depth charges. After this the U Boat had to surface and was captured with it's enigma machine and codes intact. I think it was U 512, but not sure,
