Skeletons not dropping bows on death

I made a command block farm with a summon skeleton command on a purple command block, then put the kill @e type=skeleton command in another, both using levers to activate. I expected to get mostly bones and arrows while getting bows every once in a while too. However, I never got a single bow. I went through over two full double chests and all of my hoppers, but still no bows. Please fix this, as it is the only way to get bows on the map. Please help.