I would first like to thank Propheus_D and others for their responses. And I'm going to assume erelan's comments are not directed at me. I would hardly call myself a simulationist, though I do have minimum make sense requirements for games, especially with D&D.
I suspect 2e and previous, with its much lower healing rates and greater chance of horrific damage would fit more as a comparison that 3e. 3e really began the move from damage taken to abstract hitpoints and faster healing, though 4e is a bit more divergent from the injury itself.
Let me be the first to say, I don't care if its modeling luck, stamina, etc. I just want to know that is modeling luck, stamina, etc. And in what manner it is doing so. But let us pursue the assumption that hit points are a measure of one's ability to defend one's self and resist harm. Then by logic, healing surges (poorly names as they are) are a similar effect to the hero shrugging off his fatigue and ignoring minor wounds. Would it then be reasonable to assume that rest does indeed slowly return this to him and the 6 hour requirement is only a necessary abstraction.
Tying into that, couldn't the number of encounter or daily abilities be those that you can attempt without causing yourself harm or fatique. So if you wish to continue using the Horse Cutter Strike, you could but you would deplete your reserves and weaken your ability to fight other enemies. The amount would be a matter of game balance (by the same logic open to all characters). Arcane casters could channel more energy than their body can withstand, perhaps drawing upon their life's energy. Divine casters could open themselves up to more of the divine than their form was ready to handle.
(It assumes hitpoints/healing surges are our primary resource, representing our ability). It would require two things however to work. The first is as outlined, but the second would be allowing for encounter/per day, rather than memorizing a particular ability. That doesn't quite sit for Martial abilities anyway. And since there are no sorcerors, why not?
The ring is perhaps a less clear case, as the character is unaware of their 'level' as a measure of personal power, so why it might work next week and not the previous is certainly a problem. Perhaps rather than having them not work, have them function improperly and require mastery, though why they do and the other items don't would need explaination. Or you could make them dangerous. It could be that magic beyond what you are capable of dealing with can cause you problems. Or even change the character, based on its properties.
This would require 2 things