*Awareness* as a term of the rules is checked only at the start of battle. In this case the rules of a surprise round apply.

If awareness is thought of in a broader sense, the rules on hiding might apply after the start of battle.

Rules Compendium p.92:

> If you're successfully hidden with respect to another creature, that
> creature is flat-footed with respect to you. That creature treats you
> as if you were invisible.

That means: Yes, if the character is unaware of the enemy, because the enemy is hidden, that character loses his/her Dex bonus to AC and the enemy also gets a +2 to hit.

This general rule can be used in melee ("Sneaking up from Hiding") and ranged attacks ("Sniping").

Rules Compendium p.92:

> **Sneak up from Hiding:** You can sneak up on someone afer emerging from a hiding place. For every 5 feet of open space between you and
> the target, you take a -5 penalty on your Hide check. If your Hide
> check succeeds, your target doesn't notice you until you attack or
> perform some other attention-grabbing action. Such a target is treated
> as being flat-footed with respect to you.
> **Sniping:** If you've already successfully hidden at least 10 feet from yur target, you can make one ranged attack, then take a move
> action to hide again. You take a -20 penalty on your Hide check to
> conceal yourself after the shot.

So, essentially, if the enemy is successfully hidden and closes in on the character with yet another successful hide check, he/she benefits from being hidden with his/her first attack. This implies denying the Dex bonus to AC and +2 on attack ("as if you were invisible").

This rule even seems to imply the enemy could follow up with more attacks and still benefit from being hidden in case he wins an opposed check with -20 on Hide:

> You can also take a -20 penalty on your Hide chek to hide while
> attacking, running, or charging.

This is admittedly hard to imagine and as a DM I would rule against it, but the rules seem to allow it.

The sniping option allows to hide after the shot with a move action. So if the enemy manages to win the opposed check even with the harsh penalty of -20 he could shoot the character several consecutive rounds ignoring its Dex bonus to AC and getting +2 on attack.