Saying it is a bad synchro is not explaining it correctly.
Synchros have nothing to do with keeping a gear in place, only to bring the two gears up to the same speed for engagement.
Where the confusion comes in is that the synchro drum, which contains both second and third synchros, becomes worn on the teeth that engage for second and or third gear. The teeth can become shortened from the leading edge being ground off from a bad synchro, or they can become worn at a taper from trans misalignment. Both will cause a transmission to jump out of gear.
