I've been on a forum dive recently, getting back into Pathfinder after a long hiatus, and one thing I've seen come up several times with much confusion is whether or not iterative attacks after the first can benefit from sneak attack damage, so here's a quick guide.
It depends on the situation.
Short version: If the thing you're using to set up sneak attack breaks on the first attack, later attacks don't gain sneak attack. If whatever is enabling your sneak attacks persists after the first attack, the later attacks do gain sneak attack.
Long version...
Starting combat with a sneak attack: During the surprise round, you can't full attack, so you only get one sneak attack. However, if your target didn't act in the surprise round AND you out-speed them in round 1, you could full attack them then and get sneak attack every time because they're still flat-footed. (Caveat: Unless it's been errata'd or your GM gives you the look when you try, you can use a method of gaining pounce or "virtual pounce" and use a partial charge to make a surprise-round-charging-full-sneak-attack...)
Stealth, vanish, invisibility, or feint: Usually, mid-combat, these options only grant one sneak attack. Feint only causes the target to be flat-footed "for the next attack", and you break out of Stealth or drop your vanish or invis spell when you attack. Improvements to feinting can make it count for more.
Improved invisibility, darkness/deeper darkness, mist/fog effects: Improved invis allows unlimited sneak attack against any foe that can't treat you as visible (blindsight or tremorsense, scent with certain upgrades, or a see invis or true seeing spell). Darkness and concealment effects will allow unlimited sneak attacks if and only if you have a way to ignore them (darkvision, blindsight, watersight, etc). Remember you cannot sneak attack a target with concealment, so you must be able to beat that concealment. Also, many mist/fog effects don't grant total concealment when you're adjacent to your target, so while you can Stealth with just concealment, it will still break when you attack - you need total concealment to enjoy unlimited sneak attacks.
Flanking: As long as you have your flanking bonus, sneak attacks forever. Bonus points if you have an artificial flank set up (a spell that makes your opponent flanked without needing a teammate to actually stand there) or a good tank teammate with a way to stop the bad guy from attacking you.
Other situations: Refer to "Short version" above. As long as the target is still denied their Dexterity bonus to AC and don't have cover or concealment against your attack, you can keep sneak attacking.
I sincerely hope this was helpful ^_^ have fun proving all the "rogues so underpowered" peeps wrong!
(Whatever you do, do not build a Waves Oracle 1 / Unchained Rogue X with the watersight revelation and obscuring mist known, build for ranged and two weapon fighting, pick up two of the dartguns from the Emerald Spire, and lay down ranged-with-total-concealment full-sneak-attacks with poisonous dartguns that hold entire magazines of darts from within the safety of the magic mist. It's only funny until you pull grudge monsters...)
