Saeviomagy
Adventurer
Now lets consider an adventurer is blind, but has fled the battle to wait for the blindness to wear off. A bandit is sneaking up on him, with total concealment due to the blindness. (If I understand it, the identical situation could occur at night without special vision, or with an invisible creature, or in dense fog, or any other situation with total concealment.)
The bandit makes a Stealth check to sneak. The adventurer makes a Perception check. If I understand it, if the bandit wins, the adventurer does not know that a bandit is present. If the adventurer wins, he knows the square the bandit occupies. There is no way for the adventurer to hear that there IS a bandit nearby but not know precisely where the bandit is, which I claim SHOULD be the most likely outcome. Or am I wrong again?
Part of this is caused by D&D's assumption that you're either in combat or out of it.
Specifically, if the player in question was out of combat and this scene occurred, either the bandit would take a surprise attack out of nowhere, or he would use his surprise action to maintain his stealth while moving into position and initiative would start. The player would then automatically know that something is going on (he rolled initiative) and would most likely start with perception checks to ascertain what.
In the situation you describe, this doesn't happen because there's an ongoing combat and the player never drops out of initiative. I guess you should probably rule that if someone is far enough out of a combat, he no longer has an initiative (but still acts once per initiative pass) and needs to reroll his initiative when he rejoins.
Or you can change the stealth rules to reflect the "something is up" state of alertness like others have posted.