Hello my name is Matt and I will be more than happy to assist you.
Are you able to go the front wheel off the ground to do a check so we can determine if the problem is in the front differential or the transfer case.
If you drive it for a while when it is below 32F and the vehicle is warmed up will the 4X4 drive work?
When you shift it to 4 wheel low what does the indicator light do?
When it says you are in 4 wheel low and you put it into gear. Does the vehicle take off like it is in 4 low, but with out the front wheels engaged or does take if like it is in 2 or 4 wheel mode.
Or in other words with the indicator showing you in 4 low do you still have the gear reduction like when the system is working properly.
If you are getting the gear deduction.
By gear reduction I mean the vehicle takes off faster in 4 low than it would if it is in 2 or 4 high mode or if you are driving in 4 low at 3000 RPM's you are moving 15 MPH, but in 2 or 4 high at 3000 RPMs you are moving 30 MPH.
If yes then the transfer case is good and your problem is the Front Differential Actuator
I meant to say the problem is in the Front Differentail Actuator system. Which includes the Front Differantail Actuator, the Wiring, and the Transfer Case Control Module.
Every time you use the 4X4 and It does not work has it been snowing and wet freeze out side?
The only way to verify the cause is to do these test listed on the link below at the time it is acting up. Click on link below
Front Axle Will Not Engage
Chevy Technician
10+ years automotive tech, 5 years of experience in a GM dealer