what would keep the transmission from upshifting when accelerating?
automatic transmission on 1997 Mercury Sable
Easiest thing is to check the oil level, if this is ok you need to see if shift cable is okay, do you feel the normal resistance when moving the shifter? Do you notice any sounds when selecting gears? From this point you need to determine if the drive axles are okay, if they are then you need to have the engine control module scanned for diagnostic trouble codes,(dtc's) then you need to follow diagnostic procedures to eliminate the trouble codes that would cause the transmission not to work. You may have an internal fault in the transmission or a torque converter issue. As you can see, there are many things to cause your symptoms, it is best to find a reputable shop to diagnose your concern. Good luck.