i had that exact problem on my 87 and the cause was the plastic gear on the governor was completely stripped off. i changed it and have not had any problem since.My 1987 had the same problem; I though it was the vacuum modulator. This transmission does not have a vacuum modulator. Instead it has a "governor". Located in the rear of the transmission (output shaft) on the driver side. Pop off the cover with a screwdriver, grab the square sheetmetal bracket, twist and pull. Install is just reverse. Be sure to check fluid level and condition as mentioned in another answer here. Mine was $45 for the part and 15 minutes of work.THE ABOVE IS THE CORRECT ANSWER. Just had an 88 Suburban w/700R4 not shifting out of 1st gear and I pulled the round cover off the driver's side of the trans and pulled the governor out with a twist. The plastic gear on the end was all chewed up. popped a good used one in and the burban shifts perfectly now.
Had the same issue in a 97 Suburban. Thought the transmission was slipping. Turns out it was just a dirty fuel filter. THIS WILL NOT KEEP THE TRANS FROM SHIFTING.
One thing you can check is your transmission fluid level, and condition of the fluid , if it smells burned or if it is a dark reddish-brown color it should be changed don,t forget to change the filter , you out
Check the sun shield to see if it needs replacing. You can tell if the gears are stripped by looking in the transmission pan to see if there are metal shavings in the fluid or bottom of the pan. you can also heck your shift solenoids.
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