Why only mitochondria and plastids?
There are. But they are not that universal. See kappa-particle in Paramecium and Wolbachia in insects. Also, there are different origins of plastids (compare red algae and green algae). Some organisms like Rhopallodia gibba even have plastids of multiple origin.


  So do most organelles just lose all their DNA? Or is it something that
  occurs fairly rarely?


The organelles of endosymbiotic origin lose their genes gradually. The extent and rate of loss is correlated with the number of organelle the cell harbours. The limited transfer window hypothesis speculates a probable mechanism.