Ask the Evil DM Question - How to prevent exploitation of low healing?

Got a question today from someone named "Kind of Matthew Mercer but Ginger" in the old email box asking advice about the healing system, death blows and how his players are using the heal for 1 hp to bring a character back from death saving throws.

The problem as he saw it in his game was during a combat encounter, a player who had a paladin, was using a lay on of hands (1 HP) saving a downed fighter who was in the "death saves" phase of his "life". 

It seemed like every time this fighter got knocked down to begin his death saves, the paladin would do the old 1 hp save and up goes the fighter, ready for action. 

This DM sees this as an in game exploit of the rules and is not happy with it... Maybe he's out to kill the characters or at least have them fear for their character's lives for once? Its hard to say based off of an email, but as an EviL DM myself, its always nice to see players fear their character may die, and the fact that this whole heal can be done, does not put any fear into the possible death. Which results in players thinking that their characters are "superheroes" and nothing can stop them.

In my game and older editions of D&D (pre 2000) the game was deadly, and players learned not to have their characters blindly run into things. With this whole "Balance" and "fairness" crap that 4e introduced (and continued into 5e), players can expect, "I am level 1, so the monsters will be around that level and I may die only if I really roll badly." 

Nope.

So back on track here, how do we prevent this situation from happening, which apparently is really bothering this DM, and when he changes up a bit, his group whines like a bunch of children saying "he's not fair. WAAAAAAAAAAAAAAAAAAAAAAAAAAH!"

Want to start this part off by saying, "you are the DM, its your world, your story, your rules."

He did say in his email, that he changed the rules a bit to go back to negative hit points, and you need to heal that much to get back to zero, which is how it was done back in older editions. 

You'd get hit and you'd go negative, and from there, every round you're in negative, you start "bleeding out" and your HP declines by -1 each round towards -10, and that's when you are DEAD. If you get a heal, you get that much back going towards zero, and you are stabilized and no longer bleeding out. Once you get above 0, you can get back up.

Apparently he has tried this and the group cried. So how can he fix it so everyone is happy?

I say, keep the rules as is, and allow this "exploit" to be used as is, but include in the rules a random roll of a d6 of being stunned, not allowing him (fighter) to act for that many rounds. 

SO for example, the fighter is downed, the pally heals him for the 1 HP, you as the DM roll a d6 (or a d4) and that's how many rounds the character is stunned after being at death's door, coming back to life. 

I would do this after the 3rd time of falling and getting healed, because getting a death blow, and getting back up and then again will put a little shock to the system (hey remember system shock rolls?).

This adds a little more grit to your game, allows you to keep the system in place and prevents the majority of whining, especially if you explain it as getting knocked down and back up over and over. 

Evil OUT!