Don't pat her head. Give her a good scratch under the chin and around the sides of the chin under her ears/below her jawline, which reinforces her to keep her head up. Patting on the head is a submissive reinforcment in that you are forcing her to keep her head down.
BTW, don't pet her when she is scared. That also reinforces the nervous behavior. When you do this you are telling her it is okay to show fear.