Q142 Can you persist a spell, then extend it to make it last 48 hours?
I suppose so. The FAQ has mentioned that a twinned maximized spell deals double max damage, so you are apparently allowed to determine the order in which the feats affect the spell (which I assume will be in a manner most advantageous to you).
If anything, only the empower/maximize entry seems to mention anything to the contrary, so we can safely assume that is a special case limited only to interactions between these 2 feats.
So yes, you could have persistent spell apply first to extend its duration to 24 hours, then apply extend spell to double that to 48 hours.