There's nothing in the rules that says if your position is known you can't attempt to hide again.
I'm not claiming this. What I am saying is if your attempt at hiding will inevitably result in a situation where your location is still known, then your "attempt" is most certainly a failure. You have not hidden. No die roll (and thus no Hide attempt) is needed. You can "take the Hide action" all you want, but the outcome (failure) does not depend on the result of a contested check, so it really isn't the Hide action, is it?
As long as I meet the requirements of not being able to be seen clearly (or whatever requirements halflings and wood elves have) I can attempt to hide again.
That is not the only requirement of hiding. The first requirement is that the DM must decide that circumstances are appropriate for hiding. Hiding, like the other words in the rulebook, should be understood to retain its natural English language meaning, in the sense of concealing oneself from the
notice of others. Without the DM's agreement that there is some means present of being unnoticed, any attempt to do so is irrelevant.
At that point, you can't tell I'm still there. The fact that I have nowhere to go isn't really relevant. As I said before, there may not be much benefit to me hiding, because as soon as I move I reveal myself again, that doesn't change the fact that I was hidden.
The lack of any clear benefit may be an indication that hiding is inappropriate in this situation. Think about playing hide and seek. If someone who's "it" is cheating, and watches as you go to your hiding place, instead of covering his eyes, then you aren't hidden from him. He knows where you are, even if he can't see you anymore.
Logic is exactly what it is. You can't perceive my location with your senses so you deduce I'm still there because that's where you saw me last.
Logic and reasoning are distinct from memory. No deductive reasoning is required to access information that I have directly experienced and held in my immediate awareness. That is what is called short-term memory.
*blink*
*blink* *blink*
This is quite possibly one of the most ridiculous arguments I've ever heard in my entire life. I actually laughed out loud at its lunacy. No, you can't perceive my location with your memory. It's not a sense.
It's not a sense, and yet memory, along with the senses, is one of the processes by which you become aware of and interpret your surroundings. That is perception.
Besides, memory is Intelligence, not Wisdom (PHB, pg 177 "An Intelligence check comes into play when you need to draw on logic, education, memory, or deductive reasoning.")
I would suggest that here the rules are referring to long-term memory, the ability to recall information that was stored in the past.
Sure there is, because the rules specifically say there is.
The rules say she can hide in this situation provided that the DM has decided that hiding is possible and that she is not seen clearly.
Naturally Stealthy does not override the preconditions for hiding but only says that she may attempt to hide in a situation where other characters may not. Lightfoots must still satisfy any conditions for hiding in that situation that other characters must satisfy in situations where they are allowed to hide.
The fact that she has nowhere to go is completely irrelevant to her ability to hide. Hiding and movement are completely separate in this edition. Hiding is an action in 5e, that's never been the case before, it's always been tied to movement. That's not the case anymore.
In case there's any doubt, I am not working with any preconceptions based on earlier versions of the game.
With that being said, I think you'd find that the game runs more seamlessly if movement and action are considered to happen continuously throughout one's turn, rather than inhabiting different segments of time. One needn't stop moving, for example, to attack.
There's nothing in the rules that supports this. There is one requirement to be able to attempt to hide, that your target can't see you clearly, and in the halfling's case, the very specific "You can attempt to hide even when you are obscured only by a creature that is at least one size larger than you."
Once again, that is not the only requirement of hiding, and in the halfling's case, being able to hide in a situation where others cannot does not let the halfling hide without regard for factors that would prevent any hide attempt in the first place.
There's nothing in the rules that supersedes that, nor is there anything that having your position known prevents you from attempting to hide. Being discovered makes you lose the benefits of being hidden, but that is, in no way, the same thing as not being allowed to hide if your position is known.
I'm not saying that. Obviously you are meant to be generally able to hide in a situation where your position is known before you hide as long as you are not seen clearly. I believe that this is the case because if you are not seen clearly then the creature from which you are hiding may lose sight of you as you attempt to hide. What I am saying, however, is that if after you try to hide you will, with certainty, still be seen, or if your location will still in fact be known, then you are not hiding. Resolving such attempts in the same manner as you would those which do have the potential to result in the hider's location being unknown, i.e. as you would resolve someone taking the Hide action, will give nonsensical results.
For example, what if a human attempts to hide in a dimly lit corridor relying only on being lightly obscured, because, as you have said, he only needs to not be seen clearly in order to attempt to hide? The DM calls for a Stealth check which beats his opponents Perception, and declares that he is hidden. The rules state that he now gains the benefits of being hidden. Attacks against him are at disadvantage and his opponents need to guess where he is. He gets the "Unseen Attacker" advantage on his attacks against them.
Of course this is complete nonsense because he is not unseen. He has not turned invisible. (AFAIK being hidden does not impart the Invisible condition.) His opponents are still looking right at him through the gloom since he is still only lightly obscured. This is obviously not what was meant.
I would suggest to anyone who understands the words hide, hiding, and hidden to be instances of gaming jargon, to take another look at the rules, keeping in mind the natural meanings of these words. I believe your game may be better for it. YMMV.