Suggestions for good mesh splitting software

The typical failure I have experienced occurs when the split lines up exactly over a mesh vertex. It seems like rhino cant decide what to do and fails as a result. Often moving the mesh or the split line slightly solves the issue however this is not always an acceptable work-around. Sometimes the cut needs to be exactly there or sometimes the mesh is so dense that a collision is inevitable. For specific examples see:

There are others but that is what a quick search of the forum turned up.

This error can also flow through to the mesh Boolean functions and cause them to fail as well.