Screws in stucco walls

I am new to Dave's Garden.
We live in a stucco house, new for us. One of our gates has the latch in the stucco wall. We've had trouble keeping the latch steady so that when the gate closes via a pump it will close on the latch and stayed closed. I found that using a 2" long screw worked, although it kept getting loose. Now the screw broke off in the wall and, of course, the latch fell down. Now the gate has no latch and swings freely - not good for keeping our dog in the yard! Not sure how to repair it. Anybody have ideas?