Conditions when the car trouble occurs
Transmission jump out of gear when the car is reversing. The gear wont stay when backing up.
Possible cause of transmission that jump out of gear when reversing
The shift linkage is faulty
The shift linkage is weak
The shift rail spring tension is weak
Troubleshooting transmission that jump out of gear
Transmission is very complex part and is very difficult to diagnose the cause of the problem when it occur especially the manual transmission.
With regards to the transmission problem when the transmission jumps out of gear during reversing usually the problem that involves is the shift linkage or the shift rail. Those two parts can cause the transmission to pop out of gear if both are faulty or out of adjustments or when the tension of the shift rail spring is weak. There are other possibilities but it can only be determined if the actual transmission is opened up and inspected by a mechanic specialized in transmission repair.
How to correct problem of transmission that jumps out the gear when reversing
This kind of work should be done by a professional therefore you have no option but to bring the car to a shop that specialized in manual transmission. Ask a mechanic to inspect the shift linkage and adjust if necessary, usually just a simple adjustment can fix the problem. However if the problem still occurs then the transmission should be open up to determine the exact cause of the problem and this will incur a costly repair, you may also try to seek for second opinion prior to agreeing to tear down the transmission. It is very expensive to have this kind of job on your transmission so be ready to shoulder all the expenses but if the transmission is still under warranty then you are safe because all the expenses will be covered by warranty.