battery fails if car is not started for 2 days

Hello, either the battery itself is not capable of being fully charged and sustaining that charge, the charging system is not doing an adequate job of charging the battery or a parasitic draw is occurring causing something to drain the battery while the vehicle is otherwise off. In any case, testing will be needed. Keep working with the most respected of the mechanics you have retained, or find a new one to help you. Keep in mind that a problem needs to be actively occurring to be diagnosed sometimes, so you may need to be patient and persistent.