Beginning at 3rd level, an enlightened fist can spend one of her daily stunning attempts to cast and deliver a touch spell as part of an unarmed full attack action. She can choose to deliver the touch spell with any single unarmed strike attack she makes during the action.
It doesn't say once per round like fist of energy. It specifically says the enlightened fist can us one stunning attempt to deliver a touch spell.
Actually it does. It says as part of an "unarmed full attack action." Since (unless you have something that allows two or more full attack actions in a round) you can only make one a round, you may only do one Arcane Fist a round. Rapid Fist doesn't allow you to make two full attacks a round, only one additional use of stunning a round as opposed to the normal one a round.
You may use on additional stunning attack (or other special attack that counts against your daily limit of stunning attacks) per round.
Wouldn't arcane fist be considered a special attack that counts against your daily limit of stunning attacks?
Yes. I hope you didn't think I was saying that if you have 10 stun attempts a day you can use AF 10 times a day in addition to your stun attempts. That's not what I meant.
Presume you have 10 stun attempts in a given day, you could then:
use 3 of them to stun in separate rounds
use another to do Arcane Fist in another round
in one round, stun twice with Rapid Fist
in another round, use Arcane fist and then do another stun via Rapid Fist
and then still have two more stun attempts left.
I presume, though, that what you're still not sure about is the "more than once per day" part?
If an ability/feat is allowed only once per day it (usually) says so. For Arcane Fist it simply says she "can spend
one of her daily stunning attempts" ... "as part of an unarmed full attack action." Since you can make more than one unarmed full attack action a day, you can do Arcane Fist as many times as you have stunning attempts per day (and can take full attack actions).
It would be like clerics turning. One way to rewrite (slightly) turning would be: "she can spend one of her daily turn checks as a standard action." Thus a normal cleric would still get multiple turn checks per day but only one per round.