Heart Failure means cardiac reserve cannot handle the body's circulatory needs. Symptoms of shortness of breath on exertion or at rest indicate levels of dysfunction.
Heart failure may become severe, life-threatening, backfilling the lungs with fluid called pulmonary edema. Emergent hospitalization may be required. "Early outpatient follow-up after hospitalization has been proposed as a means of reducing readmission rates. However, there are limited data describing patterns of follow-up after heart failure hospitalization and its association with readmission rates." 
A study investigating the impact of a physician visit shortly after hospital discharge was reported May 5, 2010 in JAMA. The purpose of the study was to see if an outpatient physician evaluation after release of a heart failure patient from the hospital would improve the chances of the outpatient avoiding rehospitalization.
Patients discharged from hospitals with higher rates of early physician follow-up have lower 30-day hospital readmission risk.
Hernandez AF, Greiner MA, Fonarow, GC, Hammill BG, et.al. "Relationship between Early Physician Follow-up and 30-day Readmission among Medicare Beneficiaries Hospitalized for Heart Failure." JAMA. 2010;303(17):1716-1722.