I've been having problems with my transfer case popping out of low side whenever I put pressure like climbing on it. It's done it ever since I bought it. High side works fine. What would cause this?

 

there is an adjustment on the lever on the t-case i had to adjust mine and works great now there was a write up on here some where on how to do it.

 

I can't be sure,
But I would suggest your plastic tabs on the shift fork are worn out.
that is letting the collar not engage fully.

 

I would go with both of the above, but generally it is the linkage. Put it in low range by hand with the adjustment bolt loose. Then make sure it is right in the cab. If it still does it afterwards, then check your engine and tranny mounts. They might be soft and allow the engine/tranny/tcase to move backward when climbing.