If it is the first time, the body will take some time to make specific anti-antibodies, the antivenom has plenty of time to bind to the poison.

On a future second time (specially if the first was recent) you could get a race between the kinetics of your anti-antibodies binding the antivenom and the antibodies binding the poison. I would expect it would still work, but with decreased effect.

Finally, and this is the way that it always works, the poison + antibodies (yours or external) end up making a bigger clump that is consumed by cells of the immune system (macrophages), so ultimately you always get an immune response (but that does not necessarily mean an allergic reaction)