It is no longer enough for hospitals to make patients healthy enough to leave. Now, as part of the Obama administration's health care overhaul, they are spending millions of dollars to keep those patients from coming back, often acting like personal assistants to help them manage their post-hospital lives. While federal statistics show the effort is beginning to reduce costly and unnecessary readmissions, a growing chorus of critics is asking whether the government policy, which penalizes hospitals that have high readmission rates, is unfair. They are also questioning whether hospitals should be responsible for managing the personal lives of patients once they are released — or whether they should focus on other ways to improve care.