Stubborn Persistence

As an action or bonus action, either before an attack roll (or the target's saving throw) or after the first failure of a spell attack (or oppositional success of a saving throw), the player can announce that they are "becoming persistent".  This means that for the next spell attack the character takes, it is made sure that the attack will succeed.  

When a player "becomes persistent", they will then roll their attack.  If it is a fail, they will continue to roll until they succeed.  Each failed roll, however, will result in 1 level of exhaustion until the caster quits pushing or succeeds.  Caster will continue to roll in the event of critical success or critical failure.  Critical success will yield the normal results, doubling dice in damage and will reduce one level of exhaustion taken, unless the caster has taken 6 levels.  A critical failure will count as two points of exhaustion, and the caster must choose to end the spell or continue.

If a caster becomes persistent against a creature who has legendary resistances, persistence may break through, should the caster choose to continue to roll continue.  If the opposing creature continues to spend legendary resistances to stave off re-rolling through persistence, persistence can outlast legendary resistance, with continued rolls.

The caster can become persistent only once per long rest and when they are fully rested/not exhausted.  If it is a new day, but the caster still has levels of exhaustion, they cannot become persistent until they are no longer exhausted.  Spells cannot heal more than one level of exhaustion per day when exhaustion is taken due to persistence. 

Persistence can continue to roll if the creature is immune, but will do no damage/additional damage of that type.

If the caster reaches 6 levels of exhaustion and will die due to this condition, the spell will then automatically hit and crit at max damage before the character then dies.  A character who dies in this manner can only be brought back via the Wish spell.