Latch on picket fence gate - in the middle?

Hi, I put up a 6 foot high dogear picket fence, with a four foot gate (and used a cross wire to stop it from sagging). Even so, the latch sticks and I have to reach over sometimes to free it. We have three dogs, and the largest (chocolate lab) pulls at the bottom of the gate to get out. She chewed right through the latch side picket, so I replaced it with a new one with a steel sleeve attached to the bottom. She still pulls the crap out of it, though. I was thinking that if I put the latch in the middle (vertically), it would secure it better. But then, if it sticks, I won't be able to reach over and free it. Any thoughts on how to do a stick-free latch? The one I have is the standard one you get at Lowes or HD, just a metal rod that goes into a free swinging catch, they run about $5.