Dog too submissive?

currently have a 1.5 year old female American Bulldog. We have one other dog at home (a male Shih-Tzu) and my AB is by all means the one in charge of the 2 of them. I have seen Duchess be a little dominant on a couple of occasions when it comes to the other dog we have at our house - which is a territorial 4 year old male Shih-Tzu. After a couple of skirmishes between the 2 dogs when Duchess was still a puppy, she made it clear that his reign of top dog was over. We socialized Duchess from the day we got her by taking her to the dog park and letting her be around different people. I know this breed can tend to be a little dominant so we let her know from the beginning that the humans were in charge in our house. When I used to take Duchess to the dog park I noticed she would be submissive and cower a lot to the other dogs. I assumed it was because she was so young. Today I took her back to the dog park after a few months of not going. She played well with a couple of Dobermans and another small dog. When a large hound approached her and decided he didn't like her for whatever reason, he/she immediately attacked her. Duchess went down on her back and the dog then proceeded to bite her around her face, neck and chest while she squeaked and kicked her legs. Now, this hound was pretty big but Duchess is ripped with muscle and I have no doubt she could have put up quite a fight if she wanted to. I was shocked that she went down on her back the way she did. Don't get me wrong - I don't want to see my dog fight, but I was a little surprised that she didn't defend herself a little more than she did. Is this just her personality? My husband works nights and we got Duchess as a sort of deterrent since we live in a city area. I have seen her bark at strangers in a way that she was definitely not playing around but I just don't understand this submissiveness with other dogs. Why doesn't she defend herself when she is attacked?

Asked by Duchess on Jul 13th 2009 Tagged aggression, submission, dogpark in Other Behavior & Training