There are a lot of good shooters that have to wear an arm guard. More with the longbow than with the recurve because of the lower brace height on the longbow. Some of it has to do with the way you're built, and some it has to do with form.
There are a couple of things that might help. Hold the longbow as if you're picking up a suitcase, so that your hand is more to the side of the grip rather than turned into it. Bend your elbow slightly, which will pull your forearm away from the string. Use good back tension, so that your forearm doesn't move toward the string on release. There are other things you could do to avoid arm slap, but the things I listed should be good for your shooting form and accuracy as well.