First check tranny fluid level. Chances are transmission can't build up enough fluid pressure to engage reverse, that might indicate a problem with the valve body, or a dirty filter. A worn pump shaft or torque converter might also cause loss of fluid pressure in the tranny but you would likely hear some whining noises or see problems in other gears. You may also have a dirty shift solenoid. I would suggest taking it to a real transmission shop, one that has a diagnostic stand and can run the tranny through its paces, and can change fluid/filter if needed. Most local shops tend to farm out tranny related stuff, so skip those and go straight to the tranny shop yourself. PS: seafoam can free up a sticking shift solenoid but you have to be careful in using that, it does not have the ability to keep a tranny running cool, and heat kills transmissions. You run seafoam for a specific amount of miles, then drop the pan and replace the filter and fluid.
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