The Reason for me has been the Revive pet. The revive pet cancels out the kill counter on the mob entirely instead of just counting it as one kill.

My assumption is the problem happens when an enemy dies while it is the enemy's turn. Since burn, poison, and reflect damage all happen during enemy's turn rather than the player's, it doesn't properly assign kill credit. Devs probably need to change how that check is performed so it also checks at the end of enemy's turn if anything has died that should give arena coin credit to the player.

It seems to happen when the final blow is done with burn, poison, and reflected damage

Confirmed. I noticed that Heroes killed by my Timothys Burn-effect do not count. I‘ve seen 3, and rarely only 2 kills this way, even when winning...