I often check the following option in the hope that it will be implemented when the report is rendered on the RS
web portal - but it never works...
I think what confuses people about these settings is that the "Row Headers" and "Column Headers" that the settings refer to are not visible if you have used a "table"-style tablix. These are only visible when using a "matrix"-style tablix.
Therefore I often see people trying to set this for tables and wondering why it does not work. As per the MSDN blog post referred to in Mike Honey's answer, if you have used a table then you have to fiddle about with the Advanced settings to get this to work.
My tip is to start with a matrix and make sure the row or column headers you want to remain visible are in the matrix row/column group areas (above and to the left of the double-dash lines). You can remove any row or column groups that you are not going to use. When you set the "remain visible" settings they should then just work as expected.