How long does damage remain on a creature?

I'm curious about the duration of combat and non combat damage?

Here is my situation:

My opponent has a Student of Warfare at level 2 (3/3 first strike) and a Knight Exemplar which makes his Student a 4/4 indestructible creature. I have enough mana producers to produce 8 mana with a Fireball in hand. I cast the Fireball announcing that X=6 and tapping to procude all 8 mana, using one red and 6 more for the casting cost and the 8th mana to target a second creature.

I choose the 2 creatures my opponent controls and the fireball deals 3 damage to each of them. This kills the Exemplar, but the Student is 4/4 and indestructible. But after combat the Exemplar goes to the graveyard and her static ability no longer effects the Student. This makes me think that the Student would then die when it becomes a 3/3 without indestructiblity again since the damage is actually enough to kill it now.

I am unsure of the outcome of this event and would like any feedback on the topic. Thank you.