Sounds like a problem with the .pup file.
When you play the game without patches, it should be using the ky.3do model (a.k.a., Kyle), and the ky.pup puppet file.
If you're having this problem with "almost every JK patch," then the problem must be in your end. Most patches that involve new keyframes use a modified ky.pup, so your player model must not be the ky.3do. Have you done any file rearranging in any of the JK subdirectories?
Try re-installing the game.
"The Beasts know much that we do not." -Ancient Jedi proverb