The Bug:
Firework explosions do not render when they occur over 64 blocks horizontally away from players on multiplayer servers. Given that they do render up to the player's render distance in single player, I believe this to be a bug. This bug also sometimes prevents Flight Duration 3 explosive fireworks from rendering for the player who shot the firework via crossbow.

Steps to reproduce:

1. Log onto any multiplayer server
2. Fill a dispenser with exploding fireworks and create a redstone line that will activate it more than 64 blocks long

3. Observe when dispenser is activated and the player is within 64 blocks horizontally of the dispenser, dispenser shoots the firework and you can see the firework explode

4. Observe when you're beyond 64 blocks horizontally the dispenser will still shoot the firework BUT you can't see the firework explode

Important Note:

This only affects firework explosions on mulitplayer servers. The behavior is not seen on single player worlds. It is also unaffected by server render distance.

Videos:

Video showing 64 block rendering bug: https://www.youtube.com/watch?v=og2gY7hI77c
Flight Duration 3 Fireworks shot via Crossbow affected by the same bug: https://www.youtube.com/watch?v=JIa5z0iNmkQ