Very long baseline interferometry observations show that the ends of the sources are moving outwards through the galactic interstellar medium at velocities of about 10% of the speed of light. Reference An & Baan 2012 http://adsabs.harvard.edu/abs/2012ApJ...760...77A
We assume that GPS/CSO sources have sufficient lifetimes (e.g. at least one million years) to grow to large size. There is strong evidence that large radio sources live at least 10 million years (e.g., Parma et al. 1999, http://adsabs.harvard.edu/abs/1999A%26A...344....7P). However, it is not clear that the sources that are observed to be small live that long.
Refutations (5) - CON To Topic
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There are too many small sources compared to the extrapolation from the large sources (O'Dea & Baum 1997, http://adsabs.harvard.edu/abs/1997AJ....113..148O). The "extra" small sources could be objects that remain small.
The expansion of the radio source will reduce the energy of the radiating particles and thus reduce the luminosity. Confinement of the radio source will keep the radio emission brighter (e.g., Barthel & Arnaud 1996, http://adsabs.harvard.edu/abs/1996MNRAS.283L..45B).
If the lifetime of the star formation is long compared to the radio source lifetime, then the lack of star formation in large radio sources compared to the small radio sources is significant. On the other hand, if the signatures of star formation are short lived (< 10 Myr), some large radio sources that were star forming then they were small have outlived the star formation episode.