When I slice this .stl Simplify3D adds top layers to the open-top box. Sli3er does not do this. Can anybody shed light on this? (Happened with 3.1 and previous version).
Your model has quite a few problems. There's a lot of surfaces facing the wrong way and a bunch of non-manifold edges (you can check this in S3D by going to Repair > Identify Non-Manifold). You need to repair your mesh first. Try using one of the online services like netfabb