In the Final Battle, do all spells have to be recast each round of combat?
From page 16 of the rulebook


  A spell or weapon that gives you a
  bonus (even one that says it lasts
  until the end of combat) only
  continues to give you the bonus while
  you devote the required number of
  hands to it. You can choose to switch
  weapons/spells in later combat rounds,
  but as soon as you “release” a spell
  or weapon, it stops working for you.
  Similarly, spells that are refreshed
  (such as at the beginning of each
  combat round in the final battle)
  cease to work and must be re-cast.


And from page 6


  Some cards exhaust themselves when used, which
  means that they are turned face down for the remainder
  of the turn. At the start of the Upkeep Phase, each player
  refreshes those cards by turning them face up. Simply
  remember that you can use face-up cards and that you
  cannot use face-down cards until you turn them face up
  again during the next Upkeep Phase.


So, exhausted spells are refreshed every round during the final battle and thus need to be recast. It's much simpler to think of the final battle as a combination of multiple combats through which damage carries over.