When mating parts together in an assembly, I would once in a while have an issue with a mate suddenly flipping to a non-desired orientation. I am now working with Motion, which requires you to carefully create mates that do not result in redundancies. Then, when I run Motion through a calculation, I often find that the mate has flipped to an incorrect orientation and I must either carefully suppress, reposition, and unsuprress all of the mates or delete them all and start over.
Theoretically, this will always be possible with the way I prepare the mates. SInce you cannot specify positive or negative, then the part can flip. Take the triad for an example, assuming an identity equal to the triad was something you wanted to affix to a cube. Assume you mate the axes of the triad to the planes of the cube, there is nothing that actually fixes the orientation of the triad from flipping. So, pretent the Z axis is behaving itself and remains aligned with the z-axis of the cube. The x and y could rotate 180deg such that the y-axis is now pointing to negative y and the x to negative x where you wanted positives.