Once per week? Really? Once per day, maybe. Once per day and it costs ki points. As many times per day as you have ki points to spend on it, but it just costs a buttload of them. But at once per week, and the initial attack to damage the target can fail and waste the attempt, and the target can succeed on his Fortitude save and the Monk still can’t try again any earlier, the Quivering Palm is so unreliable that it might as well not even be there. This needs to be able to be used more often. Take a look at the Paladin; he had abilities limited to per-weeks and they got increased, so why not the Monk’s Quivering Palm?
Or, to put it another way, let’s say there’s this hypothetical ability out there. You may use it once per game year, you have to use a full-round action to charge it up (this provokes Attacks of Opportunity), and a full-round action in the following turn to use it (which also provokes Attacks of Opportunity). You must succeed on a hit (and you have to declare your intention ahead of time and if the hit fails or if either of the two Attacks of Opportunity hit, the attempt is foiled), the target must fail a Reflex save, a Fortitude save, and then a Will save, and this ability can be foiled by Spell Resistance. But if you can get past all of that, you can slay the target (even if they’re anything from a god to the Tarrasque to the Lady of Pain).
Now, would such a hypothetical ability actually be worth anything (weighing the benefits versus the extremely absurd restrictions, limitations, and “Gotcha”s that I put in there)? No, of course not. The Quivering Palm is the same way (except less exaggerated).