I am going to guess that the problem you are encountering is that the Threshold filter is applying its criteria to cells, not points. A point will pass the threshold if an only if it is attached to a cell that matches the criteria.
By default, a cell will be removed if any of the points it is attached to is outside the threshold range. It is reasonably likely that a point that is just above the lower limit is connected only to cells with at least one other incident point below the lower limit. Since all the incident cells are removed, that point gets removed, too. You can change the All Scalars option to keep cells with any of the incident points matching the threshold range. But then you will have the opposite problem; you will pass several points below the lower limit.
If this is the issue, it is another form of the question asked here: Thresholding Nodal Information in VTK file. The solution is the same, too. Use the Glyph filter to create a separate cell for each point.