If it's the egg, I'd try it without and bake them in the oven. There's no egg in traditional falafel. It's the slow-cooking that could require it as a binder, but then again, there are plenty of egg subs out there that might work, too. A whole egg would add fat and soften the texture of the falafel while adding some rise and binding. Baking powder might be enough.
(But really, BK you should fry them.
Falafel is meant to be fried. It's just not the same. It's like baked donuts vs Kane's. No comparison.
Seriously, let me know sometime and i'll make them for you!)