The antiprotons do eventually get destroyed, but they are regenerated over time, so the number in the belts should be approximately constant. Remember there's almost no atmosphere in most of the VA belts, so the chances of the antiprotons hitting anything are obscenely low.

In general I believe antimatter annihilation reactions are easier at low speeds (positron annihilation comes to mind). When positrons are produced in decay reactions, they tend to slow down before annihilating.