Q:

Does Vow of Peace's calming aura affect the caster?

Are you affected by your own calming aura? I would think the answer is "no" since you cannot re-enter the area (so maybe you were affected by it initially, but that only lasted until someone took a swing at you).

A:

Technically yes, but only once upon taking the feat, so basically no.
The effect of the aura is described (BoED p. 48) as:

...you are constantly surrounded by a calming aura to a radius of 20 feet. Creatures within the aura must make a successful Will save (DC 10 + one-half your character level + your Cha modifier) or be affected as by the calm emotions spell. Creatures who leave the aura and reenter it receive new saving throws. A creature that makes a successful saving throw and remains in the aura is unaffected until it leaves the aura and reenters. The aura is a mind-affecting, supernatural compulsion.

"Creatures within the aura" doesn't make an exception for the character who took the feat, so they're affected the same as anyone else inside the aura (including the clause about ignoring it if they make their saving throw).
However, the effect of the aura works as the calm emotions spell, which says:

Any aggressive action against or damage dealt to a calmed creature immediately breaks the spell on all calmed creatures.

So, even if they fail their save, the first time anything takes an aggressive action against the vow-taker, the calm emotions effect will end.  Since, as the question points out, there's no way for a creature to leave the effect of its own aura (which would refresh the effect)...it will probably just never be affected again.
In most D&D campaigns, even a character devoted to peace is going to be the target of at least one aggressive action pretty early on.  So, this isn't likely to be a concern for very long.

