The Tile Council of America and the Ceramic Tile Installers of America do not recommend that tile be installed directly to plywood substrate(regardless of thickness) in a bathroom. In addition plywood manufacturers recommend a minimum exterior grade subfloor thickness of 1 1/4" (prefer 1 1/2") regardless if cement backerboard or HardiBacker is to be installed over it.
1/2" Cement board manufacturers apparently have more faith in the plywood and recommend a minimum 5/8" thick exterior grade plywood subfloor.
1/4" Hardibacker recommends a minimum exterior grade plywood subfloor thickness of 3/4".
Your substrate problem is typically of others and should be repaired accordingly. If it is installed over wood substrate or installed using an organic mastic adhesive you will have to tear out and redo to prevent future failure.