Sounds to me like a hub and slider issue. When you shift you pull/push on a cable, that moves a rail inside the transmission. Attrached to this rail is a shift fork. Attached to this shift fork is a hub/slider that selects which "gear" you asked for nicely
. If the "c" clips or little pieces (don't know the name, to lazy to look it up, but there are 3 of them, rectangular shape) are missing, broken, bent, destroyed, or don't like you, your car will pop out of gear.
Or you could have a busted shift fork, but that usually makes it STUCK in a gear (usually 3rd).
Syncro's, like mentioned, help you get the gear, not keep it.
Have fun with the trans rebuild
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