Can the HOA refuse to make repairs that the deed restrictons or CCRs say they are responsible for? No. If they persist in refusing to make repairs, you then have a potential right to sue to enforce them to perform their duties. If their failure results or impacts your specific property, then you can sue them directly for their failure to do what they are responsible for.
The typical response is to get involved in the HOA and change the problems from within. However, there are times when that is not feasible or desirable so litigation is a possible answer.