It is more than likely a rim bead leak. I'm sure your mechanic has already done it but wire brush the inner rim where the bead sits really well then use a some bead sealer. Just a mention one time i came across where the rim (aluminum) had a really small pin hole just enough for the tire to loose air but never really go flat, Also try spraying some soap and water around the valve stem if there is any corrosion on the rim it can slowly leak there as well. Good luck hope you get it figured out.