xigbar
Explorer
Make a hard ruling on the specific ability, not on the general rule about free actions, or you'll shoot yourself in the foot.
I see that you already have an official answer (1/round) on the Invisible Blade. It's probably the most reasonable rule, otherwise the only other option I see would be to allow you to feint as many times you want (i.e. once per attack). Anything in between would be unnecessarily complicated for the minimal difference it would make in practice!
Now try to think what mess you'll do if you put a hard limit on free actions in general... Free actions are meant for things that are either irrelevant, or self-limited such as dropping to the ground (which you can do only once until you stand up again) or dropping objects (which normally you have up to two, one in each hand). The PHB wisely says that, should there be some more complicated scenario (e.g. you have an ability that lets you also stand up as a free action), the DM will say stop when the thing starts looking stupid (your PC wanting to drop & stand up like a rubber ball). Any hard ruling made to avoid a stupid case by the RAW can open up new stupid cases as well. And will still be mostly unnecessary.
"Okay, I want to stand up, then, I want to stand up again from the standing up and be double standing!"