Shrimp(えび) is written several different ways in Japanese. For example, there are the words commonly used in Chinese: 蝦 and 鰕. There is also a compound specific to Japan, 海老, and a kokuji, 蛯. Both of the latter contain the character for old age, 老. Is there some reason why the Japanese associate shrimp with old age?
The Japanese Wikipedia page for エビ says the following:
Apparently the use of 老 comes from the way shrimp bend forward, like an old person bending forward at the waist.