Well, I am a thorough person, so I'd figured I'd share what finally solved my problem.
The problem was with the Bat, not AntispamSniper like I initially suspected. After several attempts, using the Maintenance Center of the Bat (Folder-->Maintenance Center), it found a couple of errors and fixed them. Since then, the emails have been filtering properly.
I went back and forth with the ASS developer to find this solution, he was extremely helpful and I love his product. The Bat support, not nearly as helpful (as expected), although they respond quickly using their trouble ticket. But the ASS guy uses emails which is much more helpful in this kind of problem solving.