If it is like my 03 trailblazer, here is the scoop.
2wd is 2wd only
auto engages the front drive shaft and kicks into 4wd as needed,
this setting reduces gas mileage but is my preference on snowy days.
4hi locks it into 4wd further reduces gas mileage and is 4wd all the time.
I don’t know for a fact but think it may affect handling in an adverse way
4lo adds extra torque like when you need to pull your boat out of a pea gravel or sand launch.
My experience with the auto has been very good, I have not had a problem with constant cycling. I don’t know why this 4wd would have any more trouble than any other all the time 4wd, can you go into more detail GreasyJack?