Most likely a bad vacuum modulator or no or little vacuum reaching the modulator. Check to see if there is any vacuum going to the "can looking thing" on top of the trans. It may also be a broken or misadjusted T.V. cable going from the throttle valve to the trans. (if it has one i cant remember) Take it to an actual TRANSMISSION mechanic they cost more per hour but less likely to hear the all too common "it needs a new trans".
Are you sure that it's third it's not shifting into, and not fourth? The transmission is designed to not permit shifts into fourth (overdrive) until the engine and transmission have warmed up a bit.
A car with an automatic transmission shifts itself from 1st to 2nd to 3rd when you accelerate. You don't need to shift it...that's why they call it automatic.
In automatic transmissions the second to third syncronizers always seem to go bad first, the syncronizers are worn, bad or gone. This is common in these transmissions. Also you might check your trans fluid level, sometimes a low level will cause the transmission not to shift correctly.
The transmission may need a flush and filter, or in my 92 accord I solved the problem merely by changing the transmissions computer.
In an automatic transmission, the "2" gear selection limits the vehicle to the second gear and prevents it from shifting to higher gears. This mode is useful for maintaining power and control in situations such as driving on steep inclines or when additional engine braking is needed, such as in slippery conditions. When "2" is selected, the transmission will start in first gear and shift to second gear but will not shift to third or higher until the driver manually selects a different mode. This allows for better control while still benefiting from the automatic transmission's operation.
The 400 automatic transmission may fail to shift into third gear due to several reasons, including low transmission fluid levels, a faulty transmission control module, or issues with the governor or valve body. Additionally, worn clutch packs or bands, as well as malfunctioning sensors, can also inhibit proper shifting. It's essential to diagnose the problem accurately to determine the exact cause and ensure proper repairs. Regular maintenance can help prevent such issues from arising.
Your transmission's filter may be clogged, you may be low on transmission fluid, or the transmission may need repair or replacement. If the transmission was full of fluid, I would suggest a transmission flush, or replacing the transmission filter and fluid. If this doesn't help the transmission may actually be damaged and may need repair or replacement.
There are tiny bearings and gears that make the trans shift smoothly and keep it in the right gear and when they go bad your car can develop a rough shift slipage and even trans failure
If your transmission is not shifting into third gear and overdrive it could be a parking pawl. This prevents the transmission from rotating.
More than likely your shift cables need to be lubricated.
Check your tranny fluid. If it's full, you need to get your transmission checked. The screen could be dirty and need to be replaced, or the transmission itself could need to be repaired/replaced.
A 1990 Buick Reatta not shifting into third gear could be due to several issues, including low transmission fluid levels, a faulty shift solenoid, or a malfunctioning governor. Additionally, problems with the transmission control module or internal transmission damage could also prevent proper shifting. It's advisable to check fluid levels and connections first, and if those are fine, a professional diagnostic may be necessary to identify and resolve the issue.