"Starting at 4th level, a rogue can react to danger before her senses would normally allow her to do so. She cannot be caught flat-footed, nor does she lose her Dex bonus to AC if the attacker is invisible. She still loses her Dexterity bonus to AC if immobilized. A rogue with this ability can still lose her Dexterity bonus to AC if an opponent successfully uses the feint action (see Combat) against her."
"You can use Acrobatics to move on narrow surfaces and uneven ground without falling. A successful check allows you to move at half speed across such surfaces—only one check is needed per round. Use the following table to determine the base DC, which is then modified by the Acrobatics skill modifiers noted below. While you are using Acrobatics in this way, you are considered flat-footed and lose your Dexterity bonus to your AC (if any). If you take damage while using Acrobatics, you must immediately make another Acrobatics check at the same DC to avoid falling or being knocked prone."
Does this mean someone with uncanny dodge using Acrobatics to cross unstable terrain is not flat footed?
The word "caught" might be made into a case that a balancing character is flat-footed regardless of Uncanny Dodge. It is ambiguous. If my GM called it that way, I wouldn't fight it, but... he'd still be a jerk.
I would certainly rule that Uncanny Dodge gives its benefit in balance situations as well. There's no overriding balance concern, and Uncanny Dodge is incidentally useful at best. This is one such incident.
I think it is only meant to protect you from surprise attacks. It is anti lose dex fix. After all it does not protect you from feint.
I'd be a jerk and rule the other way, especially consider there is a Rogue Power that does that:
Ledge Walker (Ex): This ability allows a rogue to move along narrow surfaces at full speed using the Acrobatics skill without penalty. In addition, a rogue with this talent is not flat-footed when using Acrobatics to move along narrow surfaces.
It seems counter-intuitive that only Rogues that took at at 2nd level would get use out of the second half, and after 4th level nobody would.
Flat-Footed itself says:
At the start of a battle, before you have had a chance to act (specifically, before your first regular turn in the initiative order), you are flat-footed. You can't use your Dexterity bonus to AC (if any) while flat-footed. Barbarians and rogues of high enough level have the uncanny dodge extraordinary ability, which means that they cannot be caught flat-footed. Characters with uncanny dodge retain their Dexterity bonus to their AC and can make attacks of opportunity before they have acted in the first round of combat. A flat-footed character can't make attacks of opportunity, unless he has the Combat Reflexes feat.
As Lincoln pointed out, the important word her is "caught", with the intent being "caught by surprise at the start of combat".
Voluntarily walking across a narrow ledge still reduces your ability to dodge (unless you're a trained Ledgewalker).