Is it common to permanently damage your heart from one episode of binge drinking?

No: However, alcohol can cause heart rhythm disturbances like atrial fibrillation and supraventricular tachycardias that can cause serious complications, including very low blood pressure, fainting, stroke and even death. Permanent damage to the heart (alcoholic cardiomyopathy) generally comes from many years of very very heavy drinking in susceptible people, and is relatively rare.