When following the steps below, the XDC file is overwritten instead of appended when saving constraints in an Implemented design.
This issue is fixed in Vivado 2014.1.
The problem that is occurring in Vivado 2013.4 is that, in a copied project when making any change and saving constraints, the constraints that came from project_1 are dumped into project_1 and the new constraints are dumped into project_2.
This is why the XDC file is overwritten with only the newly added constraints -- the old constraints are written into the XDC file in project_1.
In Vivado 2013.4 this issue can be avoided by re-running Implementation before opening Implemented design.