If you use an empty as the rotation Mirror Object: in the Mirror Object modifier, you can use the empty's rotation to affect the mirror. Procedure described at 4:30 here.
This is not a direct solution to your problem (that really sounds like an "Apply rotation" problem), but it is a work-around that might allow you to achieve what you want.
- Remove the
Mirrormodifier and instead add an
- Add an
Emptyat the location of the original object.
- Set the
Object Offsetin the
- Rotate the
Emptyuntil you get a desired rotation.