Well, when I attempted using H2O2 I went into unexplored territory. My thought went in the way that 'why should I use potentially dangerous chlorine-containing oxidizer instead of residue-free hydrogen peroxide?' As for Seachem, they're businessmen, and not particularly honest, in my eyes. So, if they argue against H2O2, I hardly care.
Anyway, I'm using diluted H2O2 for several years already, regenerated my sacks of Purigen many times, and they still apparently work as new. I didn't perform any scientific analysis, though.
One more thing: It often takes several days until Purigen gets white again. Maybe bleach works faster, I don't know.