See if there is a Reverse Osmosis service that can come by. That will remove the calcium from the water. It takes out the salt and stabilizer too so those may need to be replenished after depending on the levels.

Scott

I doubt that is deposits from the pool water. If they were, they would be less likely to manifest on the vertical surfaces.

This is more than likely caused by efflorescence

http://en.wikipedia.org/wiki/Efflorescence

Scott,
For the most part water in Phoenix area is very hard.
Have not heard of a service here doing the RO.

As Racket said this is Efflorescence coming out of the faux rock.
If water is leaking inside of the structure, this can also help drive the efflor to the surface.

While it might very well be effervescence, what are the current pH, alk, and calcium levels?

Scott

Racket/JAPB,

Do you agree with the OP builder's solution to re-paint it? And should it continue season to season or is it an initial cure issue that will somewhat disappear?