Does it seems believable that a warrior, once in a while, can do that?Certainly yes.
Does it seems believable that he can it do every time he is attacked, simply whenever he wants it?
It's not that a fighter should be able to do that whenever he wants to, but he should be able to try to do it whenever he wants to. That was the big difference between fighter feats and spells - spells you use up but have a bigger chance of succeeding each time. A combat feat can be attempted whenever you want, but you are always going to have to be skilled enough to succeed.
For example - say you're fighting someone who's several levels below you (maybe a horde of them attacked you or something). Would it be believable in that situation that he'd be able to pull off his awesome parry attack every time he wants to? Yes, because the opponent lacks the skill to prevent it, not because the warrior himself is somehow limited in how many tries per day or encounter he has to do it.
Those kind of rules make great sense in a gameplay perspective. They make for a fun game, sure. But they don't lend themselves for the kind of believability and immersion that I look for in a PnP role-playing game.