FWIW, the way it works for me is that it automatically remembers the sort options for each project.
If I set project1 to sort by filename, switch to project2 which is sorted by date, then switch back to project1, it'll switch back to filename since that was what it was sorted by last. Same if I exit and restart Aperture.
Also, switching between browser and split view retains the same sort method.
So, I think there's something wrong with your preferences. Google for how to delete aperture preferences and see if that helps.
Alternatively, provide exact steps of what you're doing and someone can tell you whether they have the same problem or if there's a different (better) way to do what you want without having the problem.