When a half-elf character belonging to a prepared spellcasting class that is able to prepare any spells on it's class spell list (Like Cleric or Ranger) casts Paragon Surge on himself and selects the feat Sahir-Afiyun adding several new spells to his class's spell list for the duration of the spell, what happens when he prepares it? It takes 15 minutes to prepare spells as long as you prepare less than a quarter of your spell slots, assume this character is at a level high enough that he has more than enough time to prepare the spell but when Paragon Surge expires, does the spell continue to be prepared or does he lose it?
You can cast it as long as the spell remains on your spell list.
In general, as long as a spell is prepared and it's on your spell list, you can cast it as a spell. As soon as paragon surge ends, those spells are no longer on your spell list. This means you have the magical energy ready to use, but lack the knowledge of how to use it. This would be similar to how a wizard taking intelligence penalties remove the ability to cast spells you prepared: a prerequisite (the spell being on your spell list) is no longer true. You still have it, you just can't use it.
So to use the spells with that feat (or a feat like it), you could cast Paragon Surge to add those spells to your spell list, prepare a spell from that list (assuming you can do so in the time available), have that spell remain prepared (while being unable to cast it), cast Paragon Surge again (adding the spell to your spell list again), and THEN cast it.
And as a reminder, if Paragon Surge is used in this way, it can only grant that feat that day (see this FAQ.)