Do deep bruises from sports injuries last forever?

Depends what type. Most contusions are minor and heal quickly, without taking the athlete needing to be removed from the game. But, severe contusions can cause deep tissue damage and can lead to complications and/or keep the athlete out of sports for months.
No. They usually go away. Sometimes, in a case of extremely severe bruising, the skin can become discolored with a pigment from the bruising. These are usually permanent discolorations.
Usually improves. Bruises are generally from hemorrhages (leaks of blood from the injured capillaries). Although deeper bruises may take longer to resorb, they generally do with time. If anything seems out of the ordinary or is not healing properly, see your physician.