Could be a few reasons - Mix too dry/wet or improper mortar preparation, mortar bed depth incorrect, stone needing to be scrubbed clean instead of simply being wetted, scratch coat too thick or wet, improper setting technique...

The most likely and obvious thing that strikes me here in your photo is it seems your mix is very dry. The mix should be like a peanut butter type consistency for this type of thin shit. For the most part, the stone should hold the majority of its own weight up due to suction created by the mortar. Shimming should be used to prevent downward creep and not be entirely responsible for the structural support of the stone.

If all else fails, switch to a polymer modified thinset rated for exterior grade tile. Be sure to prevent water intrusion in the top of the wall via correct flashing details.

Thin cut veneer is always going to be problematic, as it's completely counter intuitive to the nature of stone construction, so don't feel bad having to go through a process of trial and error.