what actually needs replacing is not easy to tell without a CMM and a load of drawings to work with...
Not sure what you know about gearboxes. Synchro hub operation is difficult to describe without some nice pictures (I used to have some excellent ones but I don't work there anymore).
In most car gearboxes, the gears mesh all the time - shifting gears doesn't actually move the gear teeth. One of the gears is free to spin on its shaft - shifting into a gear locks the gear to the shaft and makes that gear work. Obviously you only want 1 gear engaged at a time in a manual box, and that is taken care of in the selector mechanism.
The bit that locks the gear to the sdhaft is in 'the hub'. Thats the bit with a big grooved ring/sleeve around it. The selector fork sits in the groove on the sleeve. Moving the gear lever results in a movement of the selector fork / hub sleeve.
To engage the gear, basically the hub travels past the V's on the gear and onto a 'flat' area beyond. The flats actually have a small reverse angle so that any torque (+ve or -ve) holds the hub in gear. When there is no torque the hub should be held in place by the hub detent/s.
When you go from +ve to -ve torque the load is racted on a different face of the dog and for a short period in between the hub is held by the detent.
Put simply, If a gear jumps out, then the hub isn't positioned far enough past the V to lock onto the flat area. When it is on the V part, any torque through the gearbox will force the hub backwards and out of gear.
So why does it only show a problem in one direction?? (e.g. engine braking, but not when accellerating)
The answer is very simple - the gears are helical* (at a slight angle) and therefore under load they create torque,
and
an axial load. The axial load moves the gear and the shaft across a bit, thus the flat area is in a slightly different position (i.e. further away from the hub position in one direction and nearer in the other)
* 1st and reverse are straight cut not helical - hence they make a different gear load noise. On more modern boxes only reverse is straight cut so this axial movement problem can happen in 1st gear also.
so what is needed to shift the hub far enough? It may be wear in the hub, the shaft, the gear, the fork or the selector mechanim that causes the problem. It's best to fix the actual cause (which is likely to be a combination of many worn parts) rather than to attempt to fix the symptom.
To 'work-around' a solution by modifying parts is rarely a great idea as most of the tolerances and positions are a sum of the other functions - if you shim a gear shaft axially in one direction you may assist 2nd gear but create a problem in 3rd etc.. If you modify the parts that create the hub travel stop it may work intermittently as the detent position may still be wrong (so it may work under load but not if you come off and reapply the load) etc...
As for how much longer the gearbox will last - I had a box that jumped out of 2nd on engine braking. We drove that to Gambia including a severe thrashing in the desert. To get it to stay in gear whilst the car bobbed around in soft sand etc.. the passenger needed to hold it in gear as the driver needed both hands to try and keep going the right way. On roads the driver just held it in 2nd.
