A pilot's license is one of the few remaining items that is granted for life. The FAA regulations vary on medicals, there are three classes: I, II, and III. Most GA pilots have class III medical certificates. Under the age of 40, a medical is required every three years, 40 & up, every two years.
Even if you fail your medical, you do not have your license yanked. They almost never require you to surrender your license. That doesn't mean, however, that it is legal for you to fly. The regs require both a "current medical" and a valid pilot's license (there's other stuff too, but those are the two that are relevant to your question).