MDMA is not physically addictive. However, with that being said, it is important to note that MDMA is psychologically addictive. Those who partake in the use of this substance and have addictive personalities are likely to fall into a pattern of repeated use due to the psychological effects that the drug produces.
People who become psychologically addicted to the drug and use it repeatedly for an extended period of time have difficulty feeling happy and connecting to others without the assistance of the substance. They do not go through the standard withdrawal that comes along with the psychically addictive drugs, but they do experience a comedown that is on par with that of a hangover.
With prolonged use, people who become psychologically addicted to MDMA may reduce their cognitive function, and often find that they have to work really hard to regain the full capacity of their brain function. It can take years for these people to start to feel normal again and to regain control over things like memory, processing, and control over emotions. The cognitive impairments that come with MDMA abuse are just as damaging as the physical withdrawal that people addicted to other substances end up going through.