Screws are a lot harder than wood and it doesn't take much vibration or stress for them to begin to work their way out of the wood.Rather than replacing the screw with a larger one, try this. Insert a few tooth picks and a little glue into the hole. The tooth picks should help tighten up the hole
and re-secure the screw.
Note: In more severe cases you might need to re-drill the hole, tap in a glue-covered dowel, and then drill a new pilot hole in the dowel for the screw.