Each view should save it's own sort settings. I just tested this, and it was working for me. I could have different sorts for the main view and the context view. Can you please try again?
Thanks for answering. I looked further into it, and you're right - it does work for the main view. However it doesn't work for the different search lists.
What I mean is, that I editted a few search lists - each with different creteria. I guess it is not possible to determine a different sort to every single search list.