Just to clarify, you're saying that SW is moving your plane when you use it to mate to? I've never heard of that, but anything is possible. It will probably be difficult to diagnose without having the files, but it may have something to do with how the plane was created.
Can you post the assembly and it's parts? The simplest way is to open the assembly, go to File > Pack and Go, then save to a zip folder and post that. Click on the black text "Use advanced editor" at top right of the Reply box to post files, then you'll have an option at lower right to attach files.
Just a minute ago I solved the problem by linking the plane to a sketch, but yes you are correct, SW randomly mirrored the plane when I used it as a mate reference.
Previously, the reference plane was offset from another plane, which was in turn tangent to a curved surface, and angled.
Thank you for taking the effort to reply to my question.
I'm not surprised that there was a tangent relationship involved in the problem. While I've never seen that problem with a plane, tangent (both sketch relationship and assembly mates) can certainly cause problems in other areas. I'm glad you got it fixed.
As you can imagine, I was also never confronted with a similar problem. Aparently when it comes to angular and tangent mates, SW becomes a bit glitchy and starts flipping things around.
To summarize lessons learned:
-Try to to avoid angular and tangent mates
-Try to link reference geometry to a sketch