The rogue's attack deals extra damage anytime her target would be denied a Dexterity bonus to AC (whether the target actually has a Dexterity bonus or not), or when the rogue flanks her target.
“Anytime” means exactly that: you get the sneak attack for each and every attack that meets the requirements of triggering a sneak attack. There is no cooldown or frequency limit on sneak attack.
Moreover, not only can a rogue trigger sneak attack as many times as she is eligible to, she must to maintain a significant combat presence. The damage of a single sneak attack is simply too small to make the rogue much of a threat, particularly at higher levels.
Note that some ways of triggering sneak attack invalidate themselves after the first attack, however. For example, most forms of stealth leave it very difficult to continue to be hidden after the first attack (in fact, most make it hard to make even the one attack, but the rules for stealth are kind of a mess). The invisibility spell is another obvious situation where after making one attack (ending the invisibility spell), your remaining attacks may not continue to trigger sneak attack.
But in other situations, like flanking, you can and should get sneak attack as many times as possible. This fact is the very reason why rogues like two-weapon fighting so much, to get more sneak attack in.