If I though my arguments were successfully refuted I would reconsider my belief system.

For me the problem is that this lowers the bar too much. Refuting an argument requires showing that it is false. For me, showing that it isn't necessarily true, or that it leaves out other possibilities, is enough to shake my confidence in the conclusion.

A priori reasoning requires axioms that are actually known to be true. Not "haven't been refuted" or "seems to make sense," but actually known to be true. I'd even say "as far as I know" isn't good enough, since we really don't know enough about the entire world to make definitive statements. And axioms are nothing if not definitive.

Another problem is the assumption that a priori reasoning works about the world "out there," telling us what exists in the world. It works within mathematics when you define your axioms true in a given context, but our understanding of the world, and especially the world in its entirety, is not nearly so solid.