Application of stone veneer over painted wall

You don't seem to be using the RIGHT mastic, or "construction adhesive". Construction adhesive (ie PL or similar brand name) would be about the best material for the job, because copper is a REALLY DIFFICULT material to bond to.

Try experimenting (with scrap) with other brands or types of mastic/adhesive. Certain types of PL should set up near-hard within a couple of hours.

Generally speaking when stone walls are falling apart there are two main reasons:

(1) The structure has an unsound design. This is typically the case for badly designed retaining walls which have not been backed into the hill far enough.

(2) The stone is ill-fitted.

In your case reason #2 is probably the problem. You cannot just heap two unmatched stones next to each other and fit so-called mortar in between. Mortar and cement are two different things.

The correct plan of action is to reset the wall with close fitting stones which requires an expert mason.

Alternatively you can remove all the junk the original incompetent mason put in there and then cement it all back together again. This also requires a good quality mason, although it requires a much lower level of expertise than the correct plan of action, which is why most neighborhood masons will recommend this solution. Of course, such a solution will eventually fall apart as well, but it will take so long to do so that you will no longer be present, so it will be another generation's problem at that point. They, of course, will then be faced with exactly the same problem that you have now.