Probably the transmission "valve body". Try a little transmission seal conditioner, such as Trans-X. You might be able to get a little more life from the transmission. If that doesn't work, you'll need to have the transmission rebuilt.
Check the transmission fluid for odd color or smells. If all of the forward gears work ok then the transmission fluid may not be flowing properly through the valves. The filter could be stopped up, or the bands for reverse could be worn.
If a transmission for a car becomes stuck between 1st and 2nd gear the fluid should be changed. Old fluid in a transmission can cause hard shifting and stuck gears.
Could be the type of gears used for transmission reverse gear
A car without a reverse or neutral gear needs a transmission overhaul. It is possibly due to improper fluid levels, or broken gears inside the transmission itself.
A transmission flush can replace 98% of the existing fluid with fresh transmission fluid. It basically purges the system of the old and replaces it with new. The old fluid, over time, will varnish and get sticky. A flush is designed to remove this varnish and restore better working order to the transmission. It does not effect the forward and reverse gears.
could it be low fluid
If it is an automatic transmission check the transmission fluid level. I assume it has a 4 speed overdrive transmission,if so it could be a broken reverse band or as mentioned by another tech it could also be a bad reverse shell-- which is one of the most common failures of the 4T60E transmission. Usually if the shell is broken you can pull the bottom pan and there will be large pieces of metal on the magnet. good luck
The most common cause for a transmission not to change gears, is low transmission fluid. Check the transmission fluid and fill to the full line.
Transmission fluid level possible cause. This fluid level can only be checked with the engine running and at normal operating temperature.
Because you are out of transmission fluid!! Been there, done that. Check your transmission fluid, it's probably very low. Add some and you should be good to go. You should still get your transmission checked out by a mechanic though, because you probably have a leak.
mine is jumping out in all gears but reverse i added fluid and it helped somewhat but not perfect
well, if you have problems getting it into other gears, then it could be a linkage issue. however, more thank likely, it is a transmission issue. check the fluid, make sure that it is full. (sometimes it will not go into gear if there is not enough fluid in the transmission.) otherwise, get ready for a transmission repair or replacement.