6MT Reverse Issue

[sapote]

Occasionally when going into reverse, the gear doesn’t fully engage, causing the gear to pop out.

even if you push the shifter at little harder forward?

1) Did the gear grinding when shifted before? This could cause the dog teeth having blunt points and causing hard gear engagement.
2) too delay between declutch and shift action. This allows the input shaft complete stop and then probability of dog teeth gear not line up to mesh.

Next time don't shift into 1st and move forward, just let go the clutch so the input shaft spins to a different gear teeth position, then step on clutch and shift into R with faster action, especially cold. (when tranny hot, do the opposite: shift with slower action in between.)