How do monks live with medical conditions that require regular meals?
How do they cope with this condition? 


By following a doctor's recommendation, presumably. 

For arguments sake, we could apply a relativistic approach to the meaning of "coping". Buddhist practice can be and is a valid coping strategy in certain medical conditions, provided that a medical paradigm has ran out of answers (A strictly hypothetical example: certain conditions of chronic pain).


  Are they permanently exempted from this rule?


One way to look at this is that buddhism is about making people function/feel better for the sake of themselves and their surrounding. If a dogmatic adherence to religious principles worsen a persons health, then it can't be considered kusala. 

The exempt is likely permanent for as long as health conditions remains permanent. So, if conditions changes, perhaps a new take on buddhist practice could be relevant.