The simplest is figure out if the patient falls into 1 of the 3 groups: 1) non-compliant for bizarre reasons, 2) non-compliant for logic reasons (i.e. cannot afford new medications, side-effects, etc...), or 3) a combination of 1 and 2. I can definitely understand their frustration given they see many patients per day. I don't approve of the doctor simply twiddling their thumbs the moment a patient doesn't comply as that doesn't help either party.

If the reason is either 2 or 3, there are other factors affecting the patient that the doctor doesn't know about but should try and figure out. When a doctor just gives up, the patient probably feels pretty bad about themselves, may view their medical case as unbelievably difficult for the doctor or may wonder what they did wrong.

If the reasons is 1 or 3, bizarre reasoning can be very frustrating to deal with. I don't approve psychiatrists tossing their hands up because their specialization involves mental illness, it's the topic they studied. Giving up just suggests they don't care for their practice and it's unfortunate a patient has to be on the receiving end.