So whose problem is it, slingbox or apple?
quite probably, neither.
We'll the problem is that airplay works fine with any other app but with slingbox it works slowly unless it's connected by Ethernet
it's poor network, the surest way to fix that (as has been suggested) is wired.
if you can't use wired, make sure your wireless is healthy.
try to eliminate obstacles (walls/furniture) between your router, and the devices. (you may have to move the router)
the router should be placed in an open position, and higher is better
if your router has adjustable antennas, make sure they are oriented like the manufacturer says.
try to avoid interference. If you live in a congested area, changing the channel may help.
upgrading to a newer wireless router may help.
there are a lot of outside influences that affect wireless, too many to name here. look online there are numerous guides for getting the best out of your wireless.
also when using wireless, the bandwidth is limited, so if you start browsing the web on your laptop, it takes away from what's available to be used by the slingbox.