I would really love to confirm whether or not attack spells can be extended. I agree that there can be many justifications for it, and I can make some compelling ones myself, but in the interest of balance, I do not.
There was a thread awhile back in which a caster wanted to be able to give himself flaming hands as a melee weapon for several exchanges, but the dominant understanding that attack spells can't be prolonged that way meant that we were grasping for workarounds, like making the player buy the Claws power (and of course Human Guide, because Claws are an obviously inhuman feature).
The potential issue with the Discipline checks: obviously you need to cast it successfully once to be able to prolong it. But maintaining the same Discipline check for all subsequent rounds in order to hit opponents doesn't sound right.
Maybe it would work like this:
Exchange 1: Player casts the attack spell, and his Discipline check is enough to cast the spell.
Regardless of whether or not the target escapes damage with a high Athletics check, the spell was successfully cast - it just remains to be seen whether it misses or hits, and how well.
Some GMs may insist that the player add in a shift of duration to "hold" the spell energy long enough to prolong it the next exchange.
Exchange 2: Player spends the round gathering more shifts of power and "casting" the attack spell again to prolong it a few more Exchanges. Makes the Discipline check to prolong the spell per the normal rules. Player may opt to narrate a Street Fighter "Hadoken" powerup sequence.
Exchange 3: Player makes another Discipline check, but only to hit the next target, not to successfully cast the spell.