Most individual MATLAB licenses are "perpetual" licenses, which do not expire.
Mathworks did (and might still) make available Student licenses that were only valid for 1 year or for 8 months, but those were more typically sold in campus bookstores. Most Student licenses have no expiry dates. However, Student licenses are only valid while you are enrolled in a degree granting institution (or in secondary school); after you graduate you would need to get a new license.
MOOC licenses are for limited times, but you would not purchase a MOOC license yourself.
Typical individual licenses do not expire, but it is not unusual for large organizations to negotiate limited-time licenses. For example in some organizations, it is much more difficult to make a "purchase" (those are classified as 'capital') than to contract a "service" (those are classified as 'operations').