Tire problem, need some advice
 

I got my new rims installed on Monday this week. They are the same size as the previous ones, so I kept the same tires...just moved them from the old to the new. On Wednesday my passenger side rear tire was completely flat, as in 0psi. I put the spare on and went back to the place that mounted them. When they put air in the tire and put soap around it, they found the air was leaking from all around where the tire makes contact with the outside of the rim. They took the tire off, and didn't see any problems with it so they remounted it. Again, it held air just fine for about two days before going back to 0psi.

I currently have the spare on, and am wondering what my next step should be. The tire doesn't seem like it should be the issue, since it was fine on the old rims. The shop didn't notice anything blatantly wrong with the rim either. Could something be wrong with the new rim? They took almost 10 weeks to come in, so I sure hope not. I hate having tires mounted on that rim so many times already, since there's always an opportunity for it to get scratched during the process. What would you guys do next?
Thanks.

It's must be leaking somewhere re check all over the tire and rim also re check the wheel valve stem it could be tire pressure o ring leak

We found that it was leaking all around the rim, right where the rim and tire make contact. Should I have them unmount both rear tires and swap them? That way it could eliminate the tire if that same rim went flat with the other rear tire. But that means another round of them messing with my new rims and the possibility of scratching them. I was planning on getting new tires soon, but not yet. I'm also thinking about going ahead and getting new rears to see if that fixes it.
I'm kind of at a loss right now.

Sounds like a faulty wheel. Does the inner lip where it makes contact with the bead rough?
Sanding it down well with a 1500-2000 grit might help. Not sure