- Sudden Strike, like Sneak Attack, may be triggered by any attack that meets its prerequisites. Some methods of meeting those prerequisites (e.g. hiding, the invisibility spell) are nullified after the first attack, so only the first attack gets it. Others (e.g. attacking a creature before its first action, non-invisibility forms of Invisibility) persist and allow multiple attacks to qualify.
Since it has prerequisites that are much more difficult to trigger than Sneak Attack (flanking doesn’t count), far from being overpowered, it’s actually quite underpowered compared to Sneak Attack. Moreover, two-handed weapon users out-damage two-weapon fighters even when the latter has lots of bonus damage dice: a Barbarian or Fighter can do far more damage than a Rogue or Ninja. Sneak Attack multiple times per round is necessary for a Rogue to almost keep up with a Barbarian and Fighter, but the latter two will still be superior at pure damage. And all of these classes pale in comparison to spellcasters, who could do as much or more damage if they really wanted but have much better things to do than damage in the first place.
Hitting all of your attacks for full Sudden Strike damage is extremely rare, and even if we assume average damage (six hits from GTWF, 10d6 Sudden Strike at level 19 means average 35 damage per hit, total average damage 210), a typical barbarian will have no less than +11 greater attack bonus (full BAB, no TWF penalty, Mighty Rage), which turns into +22 damage from two-handed Power Attack (and, since the barbarian does not need Dex or Wis, most likely he will have higher base Str as well, which means there is more he could convert into damage if he wanted). The barbarian also gets 1½Str to damage, which is a minimum of +12 from Mighty Rage alone, but realistically there is another +6 from the extra half again of the barbarian’s base Str (typical barbarians put everything in Str, thus 18 base Str, +5 from levels, +5 from wish or manuals, +6 enhancement for 34). That’s already +40 damage to the ninja’s +35. The ninja gets two more attacks, but his damage is also highly conditional: the target must be denied its Dex bonus to AC, and must not be immune to precision damage or critical hits.
And that’s before even getting into things like the ninja not having the barbarian’s base 34 Str, or the barbarian having more feats beyond Power Attack, or supplement materials like Complete Champion’s Pounce (which, with a lance, immediately doubles the barbarian’s damage). And the barbarian has easily twice the HP of the ninja, better saves, and better weapons (all his money in one weapon instead of split between two). So no, six Sudden Strikes a round is not overpowered in the least. It’s actually falling quite short of a simple Power Attacking barbarian.
At high levels, the game is extremely lethal; any remotely competent damage-dealer can kill anything with one full-attack. The trick is, it’s really difficult to get a full-attack, because things are very mobile and have layered defenses that prevent it from happening. And the additional conditions on Sudden Strike make it even harder to land than your typical full-attack.
If you find this unsatisfying because it makes fights very short (or very swingy), you are not alone. Unfortunately, there are no easy solutions to this problem. My own solution is quite drastic, since it relies on cutting out a rather foundational part of the system (namely, the classes, feats, and spells in the Player’s Handbook).