I have a 1988 4x4 S10 Blazer. I am having a problem my transfer case I guess is popping out of gear. After I let it sit for awhile the transfer case will work just fine. Also when I have the transfer case in 2wd is the front driveshaft suppose to turn. There is some play when I move the driveshafts by hand.

 

Are you sure the Transfer Case is popping out of gear or is it maybe the Front Axle isn't Engaging?

When you think it is disengaged, see if you can turn the driveshaft. If you cannot , then your Transfer Case is working properly BUTwhat has happened is the Transfer case is locked into 4WD but the Vacuum actuator did not pull in the Cable that locks the front axle.
It's the dumbest system that some crazy engineer can concoct to shift a vehicle from 2WD to 4WD.

 

My blazer has gotten worse. I can barely drive down the street. The shifter linkage is fine. I have checked it more than once. Could it be possilbe that the chain in the transfer case is streched out or could it be that the transfer case needs to be replaced.?