Ask a simple question, get threatened with exile? Sounds fun.
Seriously, why are almost all of you anti-bag-o-ratters so insistent on making the matter about squashing the player rather than promoting fun play?
Emphasis mine. Y'all see this? Ya see how the player gets the chance to accept the DM's judgement and get back to having fun, rather than the DM tacking a "And screw you for trying" on the end regardless of how gracefully the player accepted the DM's call? That's called being a competent DM. I'm not even saying you have to accept the "exploit." Saying concentration through things like short rests is difficult would be perfectly fair, as the rules don't define how that works and the flavor fits the mechanics you want to implement. Just be civil, and try to be fair; if you can't do that, that's on you, regardless of how much you disagree with your player's style of play.
All they want is rules unambiguous enough that I don't need to ask the DM a checklist of question on how they are feeling that day to determine if using a spell is a good idea or not. If the rules took a lot of effort to define I would probably put the blame on the player for having unreasonable expectations, BUT IT'S CLEAR YOU LOT CAN'T OFFER TWO SECONDS OF EFFORT TO RESOLVE THE SITUATION WITHOUT INSULTS. Here, I'll take a stab at it...
"If the target drops to 0 hit points before this spell ends and the target is above CR 0, you can use a bonus action on a subsequent turn of yours to curse a new creature."
TADA! Spell fixed! The DM is happy because they can make CR's such that the "exploit" doesn't work. The player is happy because the rules are consistent and they can make educated guesses at what creatures qualify.
Rule #1: The DM makes the final call on rules.
Just like it says in the DMG
The D&D rules help you and the other players have a good time, but the rules aren’t in charge. You’re the DM, and you are in charge of the game.
I don't have to justify my decision to internet rando-person, if a player questions my ruling we'll discuss it. If we can't come to an agreement (this has never, ever happened in decades of DMing) see rule #1.
No yelling in all caps needed, just acceptance that at the end of the day whether I'm DMing or playing the DM is always right.